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

Sometimes life is like a tunnel. you can’t always see the light at the end of the tunnel, but if you keep moving, you will come to a better place