#### Answer

$y=-\dfrac{7}{2}x-\dfrac{31}{2}$

#### Work Step by Step

RECALL:
The slope-intercept form of a line's equation is $y=mx+b$ where m = slope and b = y-intercept.
The given line has $m=-\frac{7}{2}$ and passes through the point $(-3, -5)$.
Thus, the tentative equation of the line is:
$y=-\dfrac{7}{2}(x)+b$
To find the value of $b$, substitute the coordinates of $(-3, -5)$ into the tentative equation above to obtain:
$y=-\dfrac{7}{2}x+b
\\-5 = -\dfrac{7}{2}(-3) + b
\\-5 = \dfrac{21}{2} + b
\\-5-\dfrac{21}{2} = b
\\-\dfrac{10}{2} - \dfrac{21}{2}=b
\\-\dfrac{31}{2} = b$
Therefore, the equation of the line is:
$y=-\dfrac{7}{2}x-\dfrac{31}{2}$