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Explanation:
First we need the slope
[tex](x_1,y_1) = (-4,2) \text{ and } (x_2,y_2) = (3,-5)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-5 - 2}{3 - (-4)}\\\\m = \frac{-5 - 2}{3 + 4}\\\\m = \frac{-7}{7}\\\\m = -1\\\\[/tex]
Then we can find the y intercept using the coordinates of (x,y) = (-4,2)
y = mx+b
2 = -1(-4)+b
2 = 4+b
2-4 = b
-2 = b
b = -2
Alternatively, you can use the other point (x,y) = (3,-5) and m = -1.
Because m = -1 and b = -2, we go from y = mx+b to y = -1x+(-2) which simplifies to y = -x-2
