Hi Brodie G.
y = (-3/4)x + 15/4
Since you have your line in Slope Intercept form, the slope, m stands out
y = mx + b
y = 4/3x + 8/3
m = 4/3
The perpendicular has a slope, m, that is the opposite inverse of 4/3 or -3/4
Your perpendicular line can start with that in the same Slope Intercept Form
y = (-3/4)m + b
that passes through the point (-7,9)
Since your perpendicular line passes through (-7, 9) we can use the coordinates to calculate b
9 = -7(-3/4) + b
9 = 21/4 + b
9 - 21/4 = b
36/4 - 21/4 =b
15/4 =b
Now we can complete your line
y = (-3/4)x + 15/4
You can graph your lines at Desmos.com to show that they are perpendicular and that the perpendicular passes through (-7 , 9)
Give it a try.
