Parallel Line Equations | MathHelp.com - By MathHelp.com
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| 00:0-1 | in this problem , we are asked to write the | |
| 00:02 | equation of the line That passes through the .3 -1 | |
| 00:07 | And is parallel to the line that has the equation | |
| 00:11 | three X -5 , Y equals 10 . To write | |
| 00:17 | the equation of a line we need a point and | |
| 00:20 | a slope so that we can use the point slope | |
| 00:23 | formula . And here we are given a point but | |
| 00:27 | we don't have a slope . Remember however , that | |
| 00:31 | if our line is parallel to this other line , | |
| 00:35 | it will have the same slope as this line . | |
| 00:39 | So our first task is to figure out what the | |
| 00:42 | slope of this line is . And we do that | |
| 00:45 | by converting its equation to slope intercept or Y equals | |
| 00:51 | mx plus B form . Remember in Y equals mx | |
| 00:55 | plus B form . Why is by itself on the | |
| 00:58 | left side of the equation . So our first step | |
| 01:02 | is to subtract three X from both sides . To | |
| 01:08 | get negative five , Y equals negative three X plus | |
| 01:13 | 10 . Then divide both sides by -5 . To | |
| 01:18 | get y equals 3 50 x minus two . Remember | |
| 01:26 | in slope intercept or Y equals mx plus B . | |
| 01:30 | Form the slope of this line or it's M . | |
| 01:34 | Is the coefficient of the X . Term , Which | |
| 01:38 | in this case is 3/5 . So this line has | |
| 01:43 | a slope of 3/5 and since our line is parallel | |
| 01:48 | to it , our line must also have a slope | |
| 01:52 | of 3/5 . Oh , So to write the equation | |
| 02:01 | of our line , we use the given .3 -1 | |
| 02:06 | With a slope of 3/5 in the point slope formula | |
| 02:12 | why minus Y ? One equals M Times Princess X | |
| 02:18 | -X one . Why minus ? Why ? One would | |
| 02:23 | be why minus and negative one ? Or Y plus | |
| 02:28 | one Equals M . Which is 3/5 . Yeah , | |
| 02:34 | Times X -X . one . Which would be X | |
| 02:39 | minus three . Yeah . To convert this equation to | |
| 02:45 | standard form , We then distribute this 3/5 through the | |
| 02:50 | princes . To get 3 50 x minus 9/5 . | |
| 02:58 | Bring down our Y plus one . Now we need | |
| 03:01 | to get rid of the fractions so we multiply both | |
| 03:04 | sides of the equation by five . Yeah , that | |
| 03:11 | gives us five . Y plus five equals three X | |
| 03:16 | minus nine . Next move the number to the right | |
| 03:20 | side By subtracting five from both sides . To get | |
| 03:27 | five y equals three x -14 . Next move your | |
| 03:33 | X term to the left by subtracting three X from | |
| 03:37 | both sides to get negative three x plus five Y | |
| 03:43 | equals negative 14 . Finally make the coefficient of your | |
| 03:48 | ex-term positive by dividing both sides by -1 . And | |
| 03:54 | our final equation reads three x minus five . Y | |
| 03:59 | equals 14 . |
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