Answer
$y=-\frac{1}{3}x+\frac{1}{3}$
Refer to the graph below.
Work Step by Step
Solve for the slope $m$ 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.
$m=\dfrac{-1-1}{4-(-2)}
\\m=\dfrac{-2}{4+2}
\\m=\dfrac{-2}{6}
\\m=-\dfrac{1}{3}$
The slope-intercept form of a line's equation is $y=mx+b$ where $m$=slope and $(0, b)$ is the line's y-intercept.
The line's slope is $-\frac{1}{3}$ so its tentative equation in slope-intercept form is $y=-\frac{1}{3}x+b$.
To find the value of $b$, substitute the x and y coordinates of $(-2, 1)$ to obtain:
$y=-\frac{1}{3}x+b
\\1=-\frac{1}{3}(-2)+b
\\1=\frac{2}{3}+b
\\1-\frac{2}{3}=b
\\\frac{1}{3}=b$
Thus, the equation of the line is $y=-\frac{1}{3}x+\frac{1}{3}$.
Refer to the graph in the answer part above.
