ALL OF GRADE 9 MATH IN 60 MINUTES!!! (exam review part 2) - Free Educational videos for Students in K-12

ALL OF GRADE 9 MATH IN 60 MINUTES!!! (exam review part 2) - By Lumos Learning

Transcript


00:0-1	Here's part two of all grown in math in 60
00:03	minutes or less . So hopefully you've watched Part one
00:05	. The algebra unit , um , got about 25
00:08	minutes left to get through the rest of grade nine
00:10	. Um , this section will be shorter than the
00:12	algebra section in the last section . Geometry over the
00:14	shortest section . Um , so this is part two
00:16	linear relations . Once again , I'm going to go
00:18	quickly through the concepts in just a few examples of
00:21	things . If you want more in depth explanations ,
00:23	go to Jensen math dot c A . There's videos
00:25	for each section there . Okay , so here we
00:27	go linear relations . So first thing you would have
00:30	looked at probably a scatter plot . Scatter plots is
00:33	a type of graph that shows the correlation between two
00:36	quantitative variables . So , for example , we have
00:38	two variables here year and movie attendance and millions .
00:42	And this is this is Canadian data . We have
00:44	two variables . It's important to understand difference between the
00:47	independent , dependent variable . If we have a table
00:49	of data and horizontal rows like this X , our
00:52	independent variable is usually the first row , and why
00:55	are dependent ? Variable is usually the bottom row .
00:58	It's important to know the difference between the two variables
01:00	, because that depends where that determines where we put
01:03	the variables on our graph . The independent variable goes
01:06	on the horizontal axis dependent on the vertical axis ,
01:10	Um , and also , um , so independent variable
01:13	is year in this one dependent variable is movie attendance
01:17	and another way to tell which variable is , which
01:21	is that . Attendance depends on the year , so
01:24	that makes our dependent variable . The year causes a
01:27	change in the attendance is another way to think about
01:29	it , so it makes it our independent variable .
01:31	If you're given data in vertical columns , remember that
01:35	X is usually given to us on the left ,
01:37	so independent on the left Y on the right .
01:39	And when we graph it , make sure you remember
01:41	that we are going to put our independent variable X
01:45	on the horizontal axis . So here's our year ,
01:47	and our dependent variable movie attendance is going to go
01:53	on a vertical axis . Dependent always goes on the
01:55	Y axis . The vertical axis independent always goes on
01:58	the x axis , the horizontal axis , and make
02:00	sure when you're choosing your scales , make sure you
02:03	choose a scale that goes up by an even amount
02:05	each time . So attendance notice that I should have
02:07	a break in here because I skipped some values .
02:11	But after that skipped values between zero and 80 it
02:13	goes up by a constant amount . Each time it
02:15	goes up by five . Each time , it's important
02:18	that your scale goes up by an even amount .
02:20	Each time and years , I started 1994 went up
02:22	by an even number of years , each time by
02:24	one year . Um , for each unit , Uh
02:28	, and why did I choose 80 to start out
02:29	for attendance while I needed my lowest value is 83.8
02:33	. My highest value is 1 25.6 . So I
02:36	needed a scale that goes at least between those ranges
02:39	. So I started at 80 and then I went
02:42	all the way up to 1 . 45 because I'm
02:44	going to be making some estimations later on this graph
02:47	and years , I started 94 I went up to
02:50	2000 and six because later we're going to making an
02:53	estimation for a year outside of our range . So
02:56	if you plot all of your points on this graph
02:59	. So this is going to represent a point on
03:00	the graph . This is going to represent a point
03:02	on the graph and so on . So in 1994
03:04	movie attendance was 83.8 million . So in 1994 83.8
03:09	would be roughly right about here . I put a
03:11	dot at that point right there , 1995 movie tens
03:15	was 87.3 million . So put a dot at about
03:19	87.3 , which is right about there and so on
03:22	. If we put a point for all of our
03:24	data values and then draw a line that shows the
03:26	trend in the data , you would have something that
03:28	looks like this have my break in my graph day
03:33	, and it would fall roughly a linear trend .
03:35	When you draw a trendline , make sure you follow
03:37	two rules . Make sure you're lying goes through as
03:39	many points as possible , and the points that it
03:42	doesn't go through like here , here , here ,
03:45	here , here , here are evenly distributed above and
03:51	below the line . So there's three above the line
03:53	three below the line . But make sure dryer line
03:55	that goes through as many as possible . The ones
03:57	that doesn't go through evenly distribute above and below ,
03:59	and you'll have a good trend line . The trend
04:01	line does not have to start at the origin .
04:03	It can start anywhere along the Y axis anywhere along
04:05	the X axis , just as long as it follows
04:07	the general trend in the data . Now we can
04:10	use that trend line to make estimations . But first
04:12	, let's describe the correlation between year and attendance .
04:16	I want to describe it in two ways . First
04:19	of all , since our line is going up to
04:22	the right , we say it's a positive correlation .
04:24	And since all the dots are fairly close to the
04:27	line , we say it's a strong correlation . So
04:29	it's a strong , positive correlation we have here .
04:31	So up to the right is positive and the dots
04:34	are close to line . So strong . So it's
04:35	a strong , positive linear correlation . And what that
04:38	tells us is that as the year increases , the
04:41	movie attendance is also increasing and now notice from our
04:45	data table there's no data for 2000 and one ,
04:47	so we want to make an estimation . I want
04:51	to make an estimation for the movie tenants using our
04:53	line of best fit . So in 2000 and one
04:56	, we go up to see where just 2000 and
04:57	1 m line of best fit it meets it right
05:00	here . We look across on ry access . That's
05:03	about right here . That's about 121 million would be
05:06	our estimation for the year 2000 and one . So
05:10	you make sure you're using your line of best fit
05:12	properly here . So 121 million And then we also
05:17	have to know , was this estimation something we call
05:20	an interpolation , or was it an extrapolation ? So
05:23	what's the difference between the two ? If we look
05:25	at the data were originally given , were given data
05:28	between 94 2000 and three ? That's the range of
05:31	our data . It goes all the way from 1994
05:34	to 2000 and three . If we make an estimation
05:37	for a year between our lowest and our highest year
05:40	, we call that an interpolation . If we make
05:42	an estimation that's outside of our range to either less
05:45	than 94 or bigger than 2000 and three , we
05:47	call that an extrapolation So we made an estimation for
05:50	2000 and one that's between 94 2000 and three .
05:53	So we call that an interpretation . Let's make an
05:59	estimation for 2000 and five . So if we look
06:02	at our line of best fit so 2000 and five
06:04	this year see where our line of best fit says
06:07	the attendance would be for 2000 and five . We
06:09	put a point on the line of Best fit at
06:11	2000 and five and then look across to the y
06:13	axis . It's about right here about 1 43 or
06:16	1 44 . I'm gonna say my estimation is about
06:20	143 . Remember , we're in millions here . Did
06:24	we use interpolation or extrapolation ? While 2000 and five
06:27	is outside of the range of data were originally given
06:29	, it's bigger than our highest value 2000 and three
06:31	. So we say that that is in fact ,
06:33	an extrapolation . Yeah , okay , next thing you
06:37	would have done and the distance time graphs . How
06:39	do we analyze the distance ? Time graphs describe motion
06:41	Well , here , have a distance . Time graphs
06:43	. If we read here , it says described the
06:45	following graph that represents a person's distance from home over
06:47	a period of time . So we have a period
06:50	of time seven minutes and the graph tells us the
06:53	distance the person is in meters from their house ,
06:56	Um , during that period of time . So at
06:58	the very beginning of the graph , when zero minutes
07:01	have elapsed there 0 m from the house , which
07:04	means they're at their house . But then two minutes
07:06	later will notice they are 100 m from their house
07:09	. So this rising line up to the right tells
07:13	us the person is moving away from their house ,
07:16	right . If they were 0 m away from their
07:18	house and now they're 100 m away from their house
07:19	, they must be moving away from their house .
07:21	So this rising line up to the right that tells
07:24	us movement away from the center or , in this
07:27	case , away from the person's house . So any
07:29	line moving up to the right is movement away .
07:31	And since it's a straight line with no curves ,
07:33	we say they're moving away at a constant rate ,
07:36	and I'm going to say this is a slow movement
07:38	compared to the next line segment because It takes two
07:42	minutes to travel 100 m in this line segment ,
07:45	but this line segment here from B to C two
07:48	minutes later , they've traveled 1 to 300 m .
07:52	They traveled 300 m in the same time it took
07:55	them to travel 100 m . So B C is
07:57	a faster movement . You can tell there between fast
07:59	and slow , because faster movement as a steeper line
08:02	, slower movement is a less steep line . So
08:05	let's describe the motion here of line segment A .
08:08	Be so up to the right , which means away
08:10	from the House . And we're going to say at
08:12	a slow , steady pace . Steady pace means that
08:16	the speed is constant . They're not changing . Speeds
08:18	are not accelerating or decelerating . NBC . The line
08:21	is still going up to the right , but it's
08:23	steeper . They're traveling a further distance in the same
08:25	amount of times they're moving faster , so we'll say
08:28	they're moving at a fast , steady pace away from
08:31	their house , so away from home at a fast
08:33	, steady pace . How about C D line segment
08:36	CD at the beginning , So at four minutes ,
08:40	there are 400 m away from their house and then
08:42	two minutes later , at six minutes , there's still
08:44	400 m away from their house . And why didn't
08:46	go up or down at all between those two ,
08:48	So the person must not have moved at all .
08:51	So for two minutes they didn't move . So any
08:53	horizontal line represents no movement . So in this case
08:58	, sorry . In this case , C d .
09:00	No movement D E is the only line segment going
09:03	down to the right . So they were 400 m
09:06	away from their house . But now they're only at
09:07	the end of the line segment there , only 200
09:09	m away from their house , they must moving towards
09:11	their house . Any line segment going down to the
09:13	right represents movement towards the sensor , in this case
09:16	towards the person's house . And it's a steep line
09:19	. So they're moving . They're moving fast towards their
09:21	house . Um , and there's no curves , so
09:24	it's at a steady rate , a constant speed .
09:27	So line segment D . E . We would say
09:30	the person is moving at a fast , steady pace
09:33	toward home and in distance time graphs . Be careful
09:37	to look for curves . If you have a curved
09:39	line , you have either an acceleration or deceleration .
09:42	You have an acceleration if the line starts off not
09:44	very steep than gets steeper and steeper and steeper and
09:47	steeper and steeper . That means their rate of movement
09:48	is increasing , so that be an acceleration . If
09:51	we have a line that starts off very steep and
09:54	then gets less deep and less deep and less deep
09:56	and less deep as we move from left to right
09:58	, that represents a deceleration . So be careful of
10:02	that when we're doing distance time graphs . Okay ,
10:05	the main section for linear relations would have looked at
10:07	Is the y equals MX plus B section . Basically
10:09	, if we have two variables that form a perfect
10:12	linear relationship , that happens when , um , as
10:15	one variable increases , Um , we have another variable
10:19	that increases at a constant rate , so one variable
10:22	is a constant multiple of the other variable . So
10:26	this equation , you would have learned all these variables
10:28	mean specifically would have learned the M represents the slope
10:31	or rate of change actually have that written right below
10:35	rate of change or called the constant variation . B
10:39	represents the Y intercept , graphically speaking or the initial
10:41	value , and we have Y and X right because
10:44	we have our two variables are have a relationship between
10:47	the two . Why being are dependent ? You know
10:49	that X being are independent . So if we have
10:51	two variables to form a linear relationship with one variable
10:53	to constant multiple , the other variable Um , we
10:57	say M is the rate of change between those two
10:59	variables . And if we have a table of data
11:01	, we can calculate them the rate of change by
11:03	figuring out what is why changing by divide that by
11:06	what X is changing by . If we have a
11:07	graph , we can figure out the rate of change
11:09	by counting our rise and dividing it by our run
11:12	and in an equation , you'll refer to them as
11:15	the slope a rate of change of constant variation .
11:18	So what we're gonna do in this section is be
11:21	able to work between the table graph and equation forms
11:24	of linear relationship . Before we do that , let
11:27	me just quickly show you what I'm talking about here
11:29	. So if we have a relationship here between distance
11:34	and time , so the distance traveled by bus varies
11:37	directly with time . So we have distance and times
11:39	are two variables distance depends on time . So distances
11:43	. Why time of exit , says the bus travels
11:45	240 kilometers in three hours or distance and our time
11:48	. Once again it travels 243 hours . But if
11:52	we want to figure out the rate of change or
11:54	the slope or constant variation where we want to call
11:56	it at the rate of change , we want to
11:57	figure out what is the distance changing by for every
12:00	one hour . So to calculate that we call it
12:02	our M . Our rate of change is m .
12:03	We do our change in Y , which is 240
12:07	in this case , kilometers and we divided by our
12:10	change in X , our independent variable which is times
12:12	of three hours . If we don't do this division
12:16	, it'll tell us how many kilometers the bus travels
12:19	for every one hour . And that's a rate of
12:20	change . We need to know what is why change
12:22	changing by everyone . Unit increase in x 024 divided
12:25	by three that gives us 80 kilometers per hour .
12:29	So the buses going 80 kilometers per hour . That's
12:31	RM . That's our rate of change . Another thing
12:34	you would have looked at before . I get into
12:37	more specific things about linear relations , as you would
12:39	have looked at between direct variation and partial variation relationships
12:43	. So there's two types of linear relationships . It
12:45	could be a direct variation relationship , where the initial
12:47	value is 00 for the relationship between the variables ,
12:53	meaning graphically . The line that represents the relationship between
12:57	two variables would pass through the origin in the equation
13:00	. You don't see anything added after the variable X
13:03	. There's nothing added off at the end Here .
13:05	You can write a plus zero if you want to
13:07	, but that's a direct variation relationship . Initial value
13:10	zero passes through the origin . The equation has no
13:13	nothing added . At the end , you don't see
13:14	a plus B because the B value is zero .
13:16	The Y intercept zero partial variation relationship has an initial
13:20	value that is not zero when x zero . Why
13:23	is something else in this case , I gave an
13:25	example of why being one when x zero , that
13:27	means graphically speaking , the line is not going to
13:29	pass through the origin . In this case , it's
13:30	going to pass through one in the equation . You're
13:33	going to see that Y intercept That initial value added
13:35	after the X and we call that a partial variation
13:38	relationship . So what we're gonna do now , we're
13:42	going to be able to given a linear relationship between
13:44	two variables . We're gonna be able to represent that
13:46	relationship between the variables in a table of values .
13:49	Um , we're going to be able to represent the
13:51	relationship using an equation , and we're going to represent
13:54	the relationship between the two variables using a graph .
13:57	So let me quickly show you those three things ,
13:59	and then we'll work at moving between those three things
14:01	. So costs to electoral work varies directly with time
14:03	. So it tells us it's a direct variation ,
14:06	and it's the relationship between cost and time . In
14:09	this case , cost depends on times that cost is
14:11	dependent . Time is independent . They charge $25 per
14:15	hour . It tells us how much it costs for
14:16	every one hour , so we know our rate of
14:18	change . We know our M value is 25 in
14:22	this case through electric work . If we want to
14:24	show this relationship in a table in a table ,
14:27	we put X on the left . Why on the
14:28	right and remember access time so they could do work
14:32	for 0123 And we can make this table as big
14:35	as we want to stop there . Those are ours
14:37	now . How much would it cost for each amount
14:39	of these hours For them to do work Well ,
14:40	if they don't work , it's not gonna cost anything
14:43	. If they work for one hour . Since they
14:45	charge $25 per hour , it's gonna cost $25 .
14:48	They work for two hours . It's going to cost
14:51	$50 right ? It's 25 bucks per hour . So
14:53	two times 25 is 50 . If they work for
14:55	three hours three times 25 75 it would cost $75
14:58	. And so on . This shows the relationship between
15:02	cost and time for this electrical company . We could
15:06	represent all these numbers who want equation . We can
15:08	make an equation that shows the relationship between X and
15:11	Y and indirect variation relationship . The equation is always
15:15	y equals MX . Any linear relationship is why equals
15:18	MX plus B , but you'll see why we don't
15:19	need to plus B for this equation , because the
15:21	initial value for this equation the cost from X zero
15:24	is zero . So we don't need the plus B
15:26	because B is zero in this case , the initial
15:28	value . The Y intercept is zero . So the
15:31	relationship between cost remember wise cost , excess time cost
15:36	is equal to $25 . That's a rate of change
15:39	times the amount of time that you work for .
15:41	And this equation shows us the relation between Y and
15:43	X for any value of X , right . If
15:45	we wanted to figure out how much it costs from
15:47	you three hours of work , you plug in three
15:49	into our equation for X £25.3 or 75 will get
15:52	cost equals $75 . We don't know how much it
15:55	costs to do 10 hours of work . You would
15:57	plug in 10 forex and we'd get cost equals $250
16:01	and so on . Now , graphically speaking , if
16:03	we were to plot these points on our graph ,
16:05	let's see what it would look like . Zero hours
16:08	of work cost $0.1 hour of work cost $25.2 hours
16:12	Costs $50 . 3 hours costs $75 . Notice how
16:15	this is going up by a constant amount each time
16:19	. That's what makes this a linear relationship , because
16:21	the rate of change is constant . And then we
16:23	would connect these points with a line to show the
16:26	relationship . And there's the graph of the relationship between
16:30	cost and time for these two variables , so we
16:34	could represent the relationship between costs and time in three
16:36	different ways . Here , in a graph using an
16:39	equation or in a table of values . All three
16:42	of those ways show the relationship between cost and time
16:44	for this electric company and notice . This is a
16:48	direct creation because it starts at 00 and goes up
16:51	by a constant amount each time . That makes it
16:53	a constant for sure . That makes it a direct
16:55	variation . Also , we have a plus zero here
16:57	that also shows us it's a direct variation , and
16:59	from a table we know it's a direct variation because
17:01	the initial value is zero Okay , let's look at
17:06	what if I gave you just a table ? We
17:08	don't know what X and y are here . We
17:10	know exes are independent wise , are different . We
17:12	don't know exactly what they are . We have a
17:13	table of values here What if I wanted to come
17:15	up in the equation to represent the relationship between X
17:18	and Y here ? What I'm going to need for
17:20	any linear relationship equation . It's always going to be
17:24	the form y equals MX plus B . I'm always
17:26	going to need to determine what is the value of
17:29	and what is the value of B to be able
17:31	to write the equation of the relationship between X and
17:33	Y . So what I'm going to do first is
17:36	I'm going to figure out the value of B .
17:38	That's the easiest thing to figure out the value of
17:40	B . That is our initial value or you'll hear
17:45	it referred to graphically as the Y intercept the Y
17:47	intercept . So that means , um , where does
17:52	it cross the Y axis ? So when x zero
17:55	, What is why ? So I'm just gonna write
17:57	that here When X equals zero . Why equals what
18:04	? And we can get that from our table when
18:06	X zero y is four . So are y intercept
18:09	our B value . Our initial value B is equal
18:14	to four . So you just look in your table
18:16	when x zero . What's why that's your initial value
18:19	. That's your y intercept . If we were to
18:20	plot this 00.4 that would be right on the Y
18:22	Axis , which makes our line across the UAE except
18:25	four . So that's our B value . Mm .
18:27	How do we figure out m from the table of
18:30	values ? Remember , I showed you equations before your
18:33	rate of change , you're going to have to figure
18:34	out what is why changing by and divide that by
18:36	what X is changing by and that will tell you
18:39	for everyone . Unit increase in X . What is
18:41	? Why changing by So to figure out the change
18:44	in y an organized way to do it is to
18:46	do your second Y value minus your first y value
18:49	. And divide that by two . Figure your change
18:51	in X to your second X value minus your first
18:54	X value . So y tu minus y one over
18:56	x two minus x one That will tell your change
18:58	and y divided by your change in X . Now
19:00	you have to take two points to be your 1st
19:02	and 2nd points . I'm just gonna choose the first
19:04	two points for it to be simple here . So
19:06	this is my 1st 20.4 So That's my first X
19:09	value . My first y value . I'll choose .
19:11	This is my second point . This is my second
19:13	X value , my second y value . If I
19:15	plug those values into my equation , I have eight
19:18	minus 4/2 minus zero , and I get 4/2 ,
19:23	which is two . So my M values to my
19:26	B values for I can write my equation by plugging
19:30	in m and B into ecos and exports . B
19:33	y equals two X plus four . This equation shows
19:37	the relationship between X and Y and notice this equation
19:41	works , right ? If I plugged in eight for
19:44	X into this equation , what should I get my
19:46	answer for ? Why to be It should be 22
19:49	times 8 to 16 plus four is 20 . It
19:51	shows the relationship between the two variables . Now ,
19:53	I just want to point out you didn't have to
19:55	choose . This is your first point . This is
19:57	your second point when you plugged into y two months
19:59	. Why ? Whenever x two , minus x one
20:02	, let's say we could have chosen any two points
20:04	. I could have chosen this one to my second
20:07	point x two y two . If I plugged into
20:09	my equation here , I would get 16 minus 4/6
20:13	, minus zero . And that would give me 12/6
20:15	, which is still the same answer of two .
20:19	So that's how to go from a table to the
20:21	equation . What if I give you an equation ?
20:23	I want you to draw the graph . Well ,
20:28	to be able to do that , we know two
20:30	things from our equation here . Em . We call
20:34	that graphically speaking . We call that our slope M
20:38	Equal Slope , which in this case is three and
20:42	any whole number is over one . And we're talking
20:44	about Slope . Remember , The top is our change
20:46	and why I'm going to call that rise . And
20:50	the bottom is our change in X . We call
20:52	that run , but where do I start from ?
20:56	Don't forget this year , that is our Y intercept
20:59	. That's our initial values . We know our graph
21:01	starts right here on the Y axis at negative two
21:04	. And then from there , I need to use
21:06	my slope of 3/1 plot more points . So that
21:09	means rise three . Run one . Remember , A
21:11	positive rise means up a positive run means right so
21:15	up . Three right one and then continue up .
21:17	Three . Right , one up , three , right
21:20	, one and two plot points on the other side
21:22	of the line . Do the opposite of up three
21:24	. Right home , which is down three . Left
21:25	one and we get more points on the same line
21:29	. Connect all the points should be on the line
21:32	if you've done it properly . And that's how to
21:34	go from the equations of the graph . Plot your
21:36	Y intercept to use your B value to plot an
21:38	intercept and use your slope . Use the rise and
21:41	the run . The numerator is the rise . And
21:42	then there's the run for rise . Counting up is
21:45	positive . Counting to the right is positive for run
21:48	. If we had a negative rise , we would
21:50	count down . If we had a negative run ,
21:52	we would count left and so on . What if
21:55	we wanted to go from a graph to the equation
21:57	? Well , there's a couple ways we can do
21:59	this . We know our equation is why cause MX
22:02	plus B and we know we're going to need to
22:03	figure out the values of M and B , so
22:06	B is easier one to find , right ? The
22:08	is just the Y intercept . It tells us when
22:10	. X zero . What's why ? So where's across
22:12	the Y axis that crosses the Y axis right there
22:13	at two . Might be value is , too .
22:16	But to calculate the rate of change , we have
22:17	a couple options . We could choose to lattice points
22:20	, so points in the corners of the boxes and
22:22	we could count are rising , are run right M
22:25	equals rise over . Run Graphically speaking . So count
22:30	your rise . To get from one point to the
22:31	other , we would have to count up 1234 Up
22:36	is positive . So positive forces arise . And then
22:39	we'd have to go to the right one to going
22:41	to the right as a positive run . So four
22:43	or two , which is two . That's fine .
22:46	But what if you wanted to go from instead of
22:51	going from here to here ? What if we wanted
22:52	to go from here to here ? We would have
22:54	to count down 1234 So that would be negative for
22:58	as our rise . And then we would have to
23:00	go left to which may get negative . Two is
23:02	our run notice . Same answer negatively by negative is
23:05	positive . It doesn't matter whether at which point you
23:08	go from , you'll get the same answer either way
23:11	. Also , you could use the method we used
23:13	before using our change in y over change in X
23:19	, which is y tu minus y one over x
23:22	two minus X one that works perfectly fine as well
23:26	, changing wise the same as rise change . Next
23:28	is the same as Run . We could just choose
23:29	our two points here . Let's say this is our
23:31	first point . So that's our X one y one
23:33	. Here's our second point x two y two .
23:36	Plug into our equation . We get six minus 2/2
23:40	minus zero . Sorry , six minus 2/2 minus cereal
23:46	. That gives us 4/2 , which is two .
23:49	So either way you get the answer of two for
23:51	M . Plug into your equation . Y equals MX
23:53	plus B , and we get y equals two x
23:55	plus to this equation shows the relation between X and
23:59	Y . Um , for this graph , uh ,
24:04	we're going to do some equations of lines algebraic li
24:07	quickly , and then we'll be done this section .
24:09	So before we do that , you have to remember
24:10	parallel lines lines in the same plane that never meet
24:13	. Parallel lines have equivalent slopes , so you have
24:16	to remember that parallel lines have equivalent slopes . Perpendicular
24:22	lines , lines that meet at 90 degrees have slopes
24:24	that are negative , reciprocal of each other . So
24:27	you have to remember that negative reciprocal roles of each
24:31	other , and I'll explain that more in a second
24:34	. So determine the equation of a line algebraic given
24:37	different information I could give you Slope member Slope is
24:41	M and one point it passes through . So I
24:44	didn't give you the Y intercept . Find the equation
24:46	of a line you always need to things you always
24:49	need . Slope y intercept . I gave you slope
24:52	. I didn't give you y intercept you can use
24:56	at this point . Every point has an X and
24:59	A Y in the equation of a line will satisfy
25:01	X and Y for any point that's on the line
25:03	. So what we can do is use this information
25:06	m x and Y plug that in for M X
25:08	and Y in the equation and then solve for B
25:10	. So if we do that , if I plug
25:12	in five for Y negative number two for M negative
25:15	four for X and Y equals MX plus B .
25:18	So I'll have something . Looks like this . Negative
25:20	1/2 negative four plus b solve for B . I
25:24	will then know the B value . I can write
25:26	my equation by plugging in for M and B ,
25:28	so I'm just gonna solve this quickly . Negative .
25:30	One times negative four is four . So we have
25:32	4/2 . I know that four divided by two is
25:35	two , so I can just write that as two
25:38	plus be moved . The tour becomes a minus 25
25:41	minus two is three . So I have three equals
25:42	. B semi final equation . I plug in for
25:44	M and R B . I have negative 1/2 X
25:48	plus three . How about here ? What if I
25:51	give you a point and I tell you it's parallel
25:53	to this line . We know parallel lines of equivalent
25:55	slopes and the slope of this line . The number
25:57	in front of the X is a one . So
26:00	I have a parallel slope , is one . Those
26:03	two lines are parallel . That's a similar parallel .
26:06	The parallel slope is one , and I have a
26:08	point on the line X and y I can use
26:11	the X y and M plug into Why goes MX
26:14	plus B and solve for B Remember So like MX
26:19	plus B negative four is why one is m Xs
26:24	four . Solve for B . It's a negative .
26:27	Four equals four plus B . Move this for over
26:30	negative four . Minus four is negative . Eight .
26:33	So my final answer Y equals one x minus eight
26:37	. So we know parallel lines have equivalent slopes .
26:39	They don't have the same y intercept , so don't
26:41	use that at all . All we know para lines
26:44	have equivalent slope so I can use the slope from
26:46	that line along with the point we know is on
26:48	our parallel line . Plug it all in sulfur be
26:51	. There's the equation of our line . How about
26:53	perpendicular lines ? So we know our line goes through
26:57	this point and it's perpendicular to this line here .
27:01	So perpendicular lines of slopes , their negative reciprocal .
27:04	So this slope is negative . 2/5 , a perpendicular
27:07	slope . There's a symbol for perpendicular perpendicular slope .
27:10	We flip the slope , so instead of two or
27:13	five , we make it five or two and we
27:15	change the sign instead of it being negative , we
27:17	make it positive So we have a perpendicular slope .
27:20	We have a point . We don't use this y
27:21	intercept at all . All we know are perpendicular slope
27:24	. Sorry . Perpendicular lines have slopes or negative .
27:26	Reciprocal . So we use that perpendicular slope . At
27:29	that point , plug into y equals MX plus B
27:33	and solve for B . So why is zero And
27:36	we know it's 5/2 and X is five and we
27:42	don't know B If we solve this equation 25/2 plus
27:47	B and sorry , last step here and moved out
27:51	25 or two to the other side . We get
27:52	negative 25/2 equals beast and my equation of my perpendicular
27:57	line . I use my perpendicular slope 5/2 X minus
28:02	25/2 . That's the equation . Alignments perpendicular to this
28:06	line and goes through that point . The only other
28:09	way I could ask you to find the equation of
28:11	a line would be if I don't give you the
28:14	slope or the Y intercept right . We need both
28:16	mean m N b . But if I don't give
28:18	you either , but I do give you two points
28:21	, the line goes through . There's only one line
28:22	that goes through these two points and we'd have to
28:25	start by finding em by figuring out our change in
28:28	y So y tu minus y one over our change
28:31	in x x two minus x one . So if
28:34	this is our first point , that's our X one
28:36	y one . This is our second point . That's
28:38	our X two y two plug into our equation .
28:41	Be careful with your science with through four minus negative
28:44	too . Over six minus four . And if we
28:50	do this , we get 6/2 , which is three
28:53	. My slope is three . So I know em
28:56	. I'm going to now next step into y equals
28:58	MX plus B . I can plug in my M
29:01	and I can choose either of these points to be
29:03	my X and Y . Let's just choose the first
29:05	one here . This is my ex and my wife
29:07	. So why is negative ? Two m s three
29:10	and my ex is four and then we can solve
29:13	for B negative two equals 12 plus B and we
29:18	would get him in . The 12 were unable to
29:20	minus 12 is negative . 14 is be the equation
29:23	of my line y equals three x minus 14 ,
29:27	and I plug in M and B that I solved
29:29	for it . And you didn't have to choose this
29:31	point . You could have chosen this point to be
29:33	your X and y here . You would have gotten
29:35	the exact same answer . Um , the only other
29:40	thing from this section B horizontal vertical lines . Let
29:42	me just very , very quickly review this . If
29:44	you have an equation , looks like this . Why
29:46	equals the number ? You don't see an X at
29:48	all what that is . That's a horizontal line that
29:50	crosses through two on the Y axis . So you
29:53	would just draw a line perfectly horizontal that crosses through
29:56	two on the Y axis . That's the line y
29:59	equals to the slope of all horizontal lines is zero
30:02	. And the Y intercept in this case is to
30:05	Why is the equation y equals two ? So just
30:08	very briefly notice that every single point on this line
30:12	has a Y coordinate of two . It never goes
30:14	up or down . Right ? This is 20.62 This
30:18	is point negative . Eight to every single Y .
30:21	Coordinate of every point on this line is , too
30:23	. That's why we say the equation line is y
30:25	equals to have about an equation that says X equals
30:28	the number you don't see a y . Well ,
30:29	that's actually a vertical line that crosses through three on
30:32	the X axis . So we would just draw a
30:35	vertical line that crosses through three on the X axis
30:38	. And that is the line X equals three .
30:41	The slope of all vertical lines is undefined . And
30:45	the Y intercept while it never crosses the Y axis
30:48	, so we would say none . Why is the
30:51	equation X equals three for this will notice every single
30:53	point on this line . Right . This is 30.0.36
30:57	This is point negative six . Sorry . Uh ,
31:02	yeah , this is 60.3 . Negative six . Sorry
31:05	. This is 60.3 negative six . This is point
31:09	three . Negative two . Notice that the X coordinate
31:14	for every point on this line is three . So
31:16	we call the line X equals three X equals numbers
31:19	of vertical line y equals the number is a horizontal
31:21	line . Slope of horizontal lines . Zero slope of
31:23	vertical lines is undefined . All right , so that's
31:27	it for linear relations . Make sure you watch part
31:30	three geometry and then you will have done all of
31:32	grade nine math

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Here is a great exam review video reviewing all of the main concepts you would have learned in the MPM1D grade 9 academic math course. The video is divided in to 3 parts. This is part 2: Linear Relations. In this video you will review everything there is to know about y=mx+b, scatterplots, and distance time graphs.

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ALL OF GRADE 9 MATH IN 60 MINUTES!!! (exam review part 2) is a free educational video by Lumos Learning.

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