Find the equation of the line that passes through (-4,6) and is parallel to the line 3x+4y=-2

Question

Find the equation of the line that passes through (-4,6) and is parallel to the line 3x+4y=-2

Answer 1

Parallel lines have the same slope.  

 

If 3x+4y = -2, then 4y = -3x-2.

 

                              y = (-3/4)x - (1/2)    Slope = -3/4

 

So, the line has slope -3/4 and passes through the point (-4,6).

 

Using the point-slope form of a line, an equation of the line is:

 

   y - 6 = (-3/4)(x - (-4))

 

   y - 6 = (-3/4)x  - 3

 

        y = (-3/4)x + 3