Answer
$\color{blue}{y=\dfrac{1}{3}x+\dfrac{4}{3}}$
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 $(-1, 1)$ and $(2, 2)$.
Solve for the slope using the formula in $(2)$ above to obtain:
$m=\dfrac{1-2}{-1-2}
\\m=\dfrac{-1}{-3}
\\m=\dfrac{1}{3}$
Thus, the tentative equation of the line is:
$y=\dfrac{1}{3}x+b$
To find the value of $b$, substitute the x and y values of the point $(2, 2)$ into the tentative equation above to obtain:
$y=\dfrac{1}{3}x+b
\\2=\dfrac{1}{3}(2)+b
\\2=\dfrac{2}{3}+b
\\2-\dfrac{2}{3} = b
\\\dfrac{6}{3} - \dfrac{2}{3}=b
\\\dfrac{4}{3} = b$
Therefore, the equation of the line is:
$\color{blue}{y=\dfrac{1}{3}x+\dfrac{4}{3}}$