SOLUTION: Find an equation of the line containing the given pair of points. (-2,-1)(-9,-4) The equation of the line in slope-intercept form is y= ? Please help me solve this problem.

Algebra ->  Linear-equations -> SOLUTION: Find an equation of the line containing the given pair of points. (-2,-1)(-9,-4) The equation of the line in slope-intercept form is y= ? Please help me solve this problem.      Log On


   



Question 994012: Find an equation of the line containing the given pair of points. (-2,-1)(-9,-4)
The equation of the line in slope-intercept form is y= ?
Please help me solve this problem.

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If you have two points, A%28x%5BA%5D%2Cy%5BA%5D%29 and B%28x%5BB%5D%2Cy%5BB%5D%29 ,
you can find the slope, m , of the line connecting them as
m=%28y%5BA%5D-y%5BB%5D%29%2F%28x%5BA%5D-x%5BB%5D%29 .

If you have the slope, m , of a line and a point, C%28x%5BC%5D%2Cy%5BC%5D%29 , on that line
(point C%28x%5BC%5D%2Cy%5BC%5D%29 can be the same as A%28x%5BA%5D%2Cy%5BA%5D%29 or B%28x%5BB%5D%2Cy%5BB%5D%29 ),
you can write the equation of that line in highlight%28point-slope%29 form as
y-y%5BC%5D=m%28x-x%5BC%5D%29 .

If you have the equation of that line in highlight%28point-slope%29 form,
you can use algebra to transform that equation into an equivalent equation
for that line in highlight%28slope-intercept%29 form by solving for y .

IN THIS CASE:
A%28x%5BA%5D%2Cy%5BA%5D%29=A%28-2%2C-1%29 and B%28x%5BB%5D%2Cy%5BB%5D%29=B%28-9%2C-4%29, so
system%28x%5BA%5D=-2%2Cy%5BA%5D=-1%2Cx%5BB%5D=-9%2Cy%5BB%5D=-4%29 , and m=%28-1-%28-4%29%29%2F%28-2-%28-9%29%29=%28-1%2B4%29%2F%28-2%2B9%29=3%2F7 .
An equation for the line in highlight%28point-slope%29 form,
using point C%28x%5BC%5D%2Cy%5BC%5D%29=C%28-2%2C-1%29 , is
y-%28-1%29=%283%2F7%29%28x-%28-2%29%29<-->y%2B1=%283%2F7%29%28x%2B2%29 .
Solving for y ,
y%2B1=%283%2F7%29%28x%2B2%29<-->y%2B1=%283%2F7%29x%2B6%2F7<-->y=%283%2F7%29x%2B6%2F7-1<-->highlight%28y=%283%2F7%29x-1%2F7%29 ,
gives you the one and only equation in highlight%28slope-intercept%29 form for that line.