Answer is equation y = x - 7
Step by step
Our points (2, -5) and (5, -2)
First we will find slope
Slope formula is
y2 - y1 over x2 - x1
-2 - -5 over 5 - 2
3 over 3 = 1 slope
Next to use one set of points and slope to find our equation using formula
y - y1 = m (x - x1)
y - - 5 = 1 (x - 2)
y + 5 = 1x - 2
Subtract 5 from both sides to isolate y
y + 5 - 5 = 1x -2 -5
y = x - 7