Answer
$\color{blue}{y=-\frac{3}{2}x-\frac{7}{2}}$
Work Step by Step
RECALL:
The slope-intercept form of a line's equation is $y=mx+b$ where $m$=slope and $(0, b)$ is the line's y-intercept.
The given line has a slope of $-\frac{3}{2}$ therefore the tentative equation of the line is $y=-\frac{3}{2}x+b$
To find the value of $b$, substitute the x and y values of the given point into the tentative equation above to obtain:
$y=-\frac{3}{2}x+b
\\4=-5(-\frac{3}{2})+b
\\4=\frac{15}{2}+b
\\4-\frac{15}{2}=\frac{15}{2}+b-\frac{15}{2}
\\\frac{8}{2}-\frac{15}{2}=b
\\-\frac{7}{2}=b$
Therefore, the equation of the line is $\color{blue}{y=-\frac{3}{2}x-\frac{7}{2}}$.
