Answer
$y=-8x-11$
Work Step by Step
RECALL:
(1) The slope-intercept form of a line's equation is $y=mx+b$ where m = slope and b = y-intercept.
(2) The slope of a line can be found using the formula $m=\dfrac{y_2-y_1}{x_2-x_1}$ where $(x_1, y_1)$ and $(x_2, y_2)$ are points on the line.
Solve for the slope to obtain:
$m=\dfrac{-3-5}{-1-(-2)}
\\m=\dfrac{-8}{-1+2}
\\m=\dfrac{-8}{1}
\\m=-8$
Thus, the tentative equation of the line is:
$y=-8x+b$
To find the value of $b$, substitute the coordinates of $(-2, 5)$ into the tentative equation above to obtain:
$y=-8x+b
\\5 = -8(-2)+ b
\\5 = 16+b
\\5-16=b
\\-11=b$
Therefore, the equation of the line is:
$y=-8x+(-11)
\\y=-8x-11$
