Answer
$3x+2y=-7$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the different forms of linear equations to find the equation of the line with the following given characteristcs:
\begin{array}{l}\require{cancel}
\text{through } (-5,4)
\\\text{m}=-\dfrac{3}{2}
.\end{array}
Use the properties of equality to express the equation in the standard form.
$\bf{\text{Solution Details:}}$
Let $x_1=-5,$ $y_1=4,$ and $m=-\dfrac{3}{2}.$
Using $y-y_1=m(x-x_1)$ or the Point-Slope Form of linear equations, the equation of the line with the given conditions is
\begin{array}{l}\require{cancel}
y-4=-\dfrac{3}{2}(x-(-5))
.\end{array}
Using the properties of equality, in the form $ax+by=c$ or the Standard Form, the equation above is equivalent to
\begin{array}{l}\require{cancel}
y-4=-\dfrac{3}{2}(x+5)
\\\\
2(y-4)=\left[-\dfrac{3}{2}(x+5)\right]2
\\\\
2(y-4)=-3(x+5)
\\\\
2(y)+2(-4)=-3(x)-3(5)
\\\\
2y-8=-3x-15
\\\\
3x+2y=-15+8
\\\\
3x+2y=-7
.\end{array}
