Answer
$y=-2x+2$
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 $m$ of the line that passes through the points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:
$m=\dfrac{y_2-y_1}{x_2-x_1}$
Solve for the slope using the formula in (2) above to obtain:
$m=\dfrac{-2-4}{2-(-1)}
\\m=\dfrac{-6}{3}
\\m=-2$
Substituting this for $m$ in the slope-intercept form gives:
$y=-2x+b$
To find the value of $b$, substitute the x and y values of $(2, -2)$ to obtain:
$y=-2x+b
\\-2=-2(2)+b
\\-2 = -4+b
\\-2+4=b
\\2=b$
Thus, the equation of the line that passes through the two given points is:
$y=-2x+2$
