Answer
$y=-\dfrac{7}{2}x-\dfrac{31}{2}$ or, in general form, $7x+2y+31=0$
Work Step by Step
Through $(-3,-5);$ slope $-\frac{7}{2}$
Use the point-slope form of the equation of a line, which is $y-y_{1}=m(x-x_{1})$, where $(x_{1},y_{1})$ is a point through which the line passes and $m$ is the slope.
Both $m$ and $(x_{1},y_{1})$ are given. Substitute them into the formula and simplify to obtain the equation of this line:
$y-y_{1}=m(x-x_{1})$
$y+5=-\dfrac{7}{2}(x+3)$
$y+5=-\dfrac{7}{2}x-\dfrac{21}{2}$
$y=-\dfrac{7}{2}x-\dfrac{21}{2}-5$
$y=-\dfrac{7}{2}x-\dfrac{31}{2}$ or, in general form, $7x+2y+31=0$
