Y-4=5/4 (x+3); (-7 8)
write the equation that is perpendicular to the given line and passes through the given point

So you are given y-4 = 5/4(x+3). This is from a form called point-slope form, written as y-y1 = m(x-x1). This gives us the slope. From looking at our original equation we see m = 5/4. To find it perpendicular, we do the negative reciprocal meaning we flip the fraction and make it a negative. So we get -4/5. So our slope is -4/5. Now we can use our y = mx + b form and substitute m and our order pair. So we get

8 = (-4/5)(-7) + b

Now we solve for b:

8 = 5.6 + b

b = 2.4

So our equation is:

y = -4/5x + 2.4