Passing through (-1, - 7) and perpendicular to the line with equation 4x + 5y = 31

4x + 5y = 31

5y = - 4x + 31

y = - 4/5x + 31/5 ... the slope here is - 4/5. A perpendicular line will have a negative reciprocal slope. All that means is " flip " the slope and change the sign. So the slope we need is 5/4 (see how I flipped the slope and changed the sign)

y = mx + b

slope (m) = 5/4

(-1,-7) ... x = - 1 and y = - 7

now we sub and find b, the y int

-7 = 5/4 (-1) + b

-7 = - 5/4 + b

-7 + 5/4 = b

-28/4 + 5/4 = b

- 23/4 = b

so ur perpendicular line will be : y = 5/4x - 23/4