What is the equation of a line parallel to the line 2x-3y=6 and that passes through the point (-6,12)

Hello from MrBillDoesMath!

y =  (2/3)x + 16

Discussion:

Given line:

2x - 3y = 6         =>   add 3y to both sides

2x = 6 + 3y        => subtract 6 from both sides

2x -6 = 3y          => divide both sides by 3

y =(2/3)x - 2  

The slope of this line, m,  (2/3) and any line parallel to the given line has the same slope.  We are looking for the line with slope (2/3) passing through (-6, 12)

y = (2/3)x + b                                => substitute (x,y) = (-6, 12) in the equation

12 = (2/3)(-6) + b                           =>  add (2/3)(6) = 12/3 = 4

12 + 4 = (2/3)(-6) + (2/3)(6) + b     => as (2/3)(-6) + (2/3)(6)  = 0

12 +4 = 0 + b    =>

b = 16

Hence the equation of the parallel line through ( -6,12) is

y = mx + b

  =(2/3)x + 16

Check: is (-6,12) on this line?  Does 12 = (2/3)(-6) + 16 =  -4 + 16 = 12? Yes!

Thank you,

MrB