Equation of a line through a given point, parallel to a second line

Question

Assume that the line passes through the point (−1,2) and is parallel to the line through the points ( 6,6) and (−3,−4).
Find the equation of this line in slope intercept form.

Answer 1

The line passing through (6,6) and (-3,-4)

has slope (-4-6)/(-3-6) = -10/-9 = 10/9

 

The parallel line must have the same slope of 10/9.

It passes through (-1,2)

So y=2, x=-1, and M=10/9

 

The equation of any line is y = Mx + b.

So the intercept b = y - Mx

                           = 2 - (10/9)(-1)

                           = 2 + 10/9

                             = (18+10)/9

                              = 28/9

 

The equation is

   y = 10/9x + 28/9