Answer
$y=-\dfrac{3}{5}x+\dfrac{14}{5}$
Work Step by Step
Point $(-2,4)$ $;$ $m=-\dfrac{3}{5}$
Use the point-slope form of the equation of a line formula, which is $y-y_{0}=m(x-x_{0})$, where $(x_{0},y_{0})$ is a point through which the line passes and $m$ is its slope.
Substitute the known values into the formula and evaluate to obtain the equation of the line:
$y-y_{0}=m(x-x_{0})$
$y-4=-\dfrac{3}{5}(x+2)$
$y-4=-\dfrac{3}{5}x-\dfrac{6}{5}$
$y=-\dfrac{3}{5}x-\dfrac{6}{5}+4$
$y=-\dfrac{3}{5}x+\dfrac{14}{5}$
The sketch of the line is shown below:
