Find the equation.

Question

Find the equation of a line that is both parallel to 5x + 6y = 20 and that goes through the point (-4,8). Give your answer in:

1. Point-slope form

2. Slope-intercept form

3. Standard form

Answer 1

Let's answer in reverse order:

 

(3) The equation 5x+6y=20 is given in Standard Form (Ax+By=C).  The slope is (-A/B) and all parallel lines have the equation 5x+6y=D and we need the point (-4,8) to find D.

       5(-4)+6(8)=D

          28=D

   The equation of the parallel line in Standard Form is:    5x+6y=28

 

(2) Slope-intercept form (y=mx+b) is y=(-A/B)x+(C/B) from Standard Form.

   The equation of the parallel line in slope-intercept form is:   y=(-5/6)x+(28/6)

 

(1) Point-slope form

   The slope of the parallel line (and the given line) is m=(-5/6).

      Point-slope form looks like:   (y-y₁) = m(x-x₁)

   The equation of the parallel line in point-slope form is:  (y-8)=(-5/6)(x+4)