Help solving problem

Question

Find the equation of the line, in slope-intercept form, that is perpendicular to -7x - 4y = 4 and contains (-6,5)

Answer 1

-4y = 7x+4 <-- adds 7x

y = (-7/4) x - 1 <-- divides by 4

the slope of the perpendicular is (4/7)

(-6,5) ---> x = -6 when y=5

intercept formula : B = y - mx = 5 - (4/7)(-6)

= 5 + 24/7

= 5/1 + 24/7

= 35/7 + 24/7

= 59/7

y = (4/7) x + 59/7

Answer 2

solve for y

4y=-7x -4

y = -(7/4)x -1

-7/4 is the slope. for the perpendicular line, you need the negative inverse or 4/7= m

y =mx+b

y=(4/7)x + b where b is the y intercept. plug in the point (-6,5) to solve for b

5 =(4/7)(-6) +b

b = 5+ 24/7 = 35/7 + 24/7 = 59/7

the perpendicular line equation is

y=(4/7)x +59/7

or

7y =4x+59