Answer
$\color{blue}{y=\dfrac{1}{5}x+\dfrac{23}{5}}$.
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 that contains the points $(x_1, y_1)$ and $(x_2, y_2)$ can be found using the formula:
$m=\dfrac{y_2-y_1}{x_2-x_1}$
Solve for the slope of the line using the two given points on the line to obtain:
$m=\dfrac{4-5}{-3-2}
\\m=\dfrac{-1}{-5}
\\m=\dfrac{1}{5}$
Thus, the tentative equation of the line is:
$y=\dfrac{1}{5}x+b$
To find the value of $b$, substitute the x and y values of the point $(2, 5)$ into the tentative equation above to obtain:
$y=\dfrac{1}{5}x+b
\\5=\dfrac{1}{5}(2)+b
\\5=\dfrac{2}{5}+b
\\5-\dfrac{2}{5}=b
\\\dfrac{25}{5}-\dfrac{2}{5}=b
\\\dfrac{23}{5}=b$
Therefore, the equation of the line is $\color{blue}{y=\dfrac{1}{5}x+\dfrac{23}{5}}$.
