Answer
$y=-\frac{1}{3}x+\frac{1}{3}$
See graph.
Work Step by Step
To calculate the slope between points $(x_1,y_1)$ and $(x_2,y_2)$, we use the formula:
$slope=m=\frac{y_2-y_1}{x_2-x_1}$
We calculate the slope between $(-2,1)$ and $(4,-1)$:
$slope=\displaystyle \frac{-1-1}{4-(-2)}$
$=\frac{-2}{6}$
$=-\frac{1}{3}$
A line in point-slope form has the equation:
$y-y_1=m(x-x_1)$
We plug in the point $(4,-1)$:
$y-(-1)=-\displaystyle \frac{1}{3}(x-4)$
And solve for $y$:
$y+1=-\displaystyle \frac{1}{3}(x-4)$
$3(y+1)=-(x-4)$
$3y+3=-x+4$
$3y=-x+1$
$y=-\frac{1}{3}x+\frac{1}{3}$
See graph.