Answer
$\color{blue}{y=-x+2}$
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 of a line can be solved 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.
The given line contains the points $(-1, 3)$ and $(1, 1)$.
Solve for the slope using the formula in $(2)$ above to obtain:
$m=\dfrac{3-1}{-1-1}
\\m=\dfrac{2}{-2}
\\m=-1$
Thus, the tentative equation of the line is:
$y=-1(x)+b
\\y=-x+b$
To find the value of $b$, substitute the x and y values of the point $(1, 1)$ into the tentative equation above to obtain:
$y=-x+b
\\1=-1+b
\\1+1=b
\\2=b$
Using the y-intercept, we find that the equation of the line is:
$\color{blue}{y=-x+2}$
