Answer
$3x-4y=-24$
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 } (-4,3)
\\\text{m}=\dfrac{3}{4}
.\end{array}
Use the properties of equality to express the equation in the standard form.
$\bf{\text{Solution Details:}}$
Let $x_1=-4,$ $y_1=3,$ and $m=\dfrac{3}{4}.$
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-3=\dfrac{3}{4}(x-(-4))
\\\\
y-3=\dfrac{3}{4}(x+4)
.\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}
4(y-3)=\left[\dfrac{3}{4}(x+4) \right]4
\\\\
4(y-3)=3(x+4)
\\\\
4(y)+4(-3)=3(x)+3(4)
\\\\
4y-12=3x+12
\\\\
-3x+4y=12+12
\\\\
-3x+4y=24
\\\\
-1(-3x+4y)=-1(24)
\\\\
3x-4y=-24
.\end{array}
