Answer
$3x+4y=10$
Work Step by Step
Using $y-y_1=m(x-x_1)$ or the point-slope form of linear equations, the equation of the line passing through $(
-2,4
)$ and with a slope of $m=
-\dfrac{3}{4}
$ is
\begin{array}{l}\require{cancel}
y-4=-\dfrac{3}{4}(x-(-2))
\\\\
y-4=-\dfrac{3}{4}(x+2)
.\end{array}
In the form $y=mx+b$, the equation above is equivalent to
\begin{array}{l}\require{cancel}
y-4=-\dfrac{3}{4}(x+2)
\\\\
y-4=-\dfrac{3}{4}x-\dfrac{3}{2}
\\\\
y=-\dfrac{3}{4}x-\dfrac{3}{2}+4
\\\\
y=-\dfrac{3}{4}x-\dfrac{3}{2}+\dfrac{8}{2}
\\\\
y=-\dfrac{3}{4}x+\dfrac{5}{2}
.\end{array}
In the form $Ax+By=C$, the equation above is equivalent to
\begin{array}{l}\require{cancel}
y=-\dfrac{3}{4}x+\dfrac{5}{2}
\\\\
4(y)=4\left(-\dfrac{3}{4}x+\dfrac{5}{2}\right)
\\\\
4y=-3x+10
\\\\
3x+4y=10
.\end{array}
Hence, the different forms of the equation of the line with the given conditions are
\begin{array}{l}\require{cancel}
\text{slope-intercept form: }
y=-\dfrac{3}{4}x+\dfrac{5}{2}
\\\\
\text{standard form: }
3x+4y=10
.\end{array}