Answer
$y=\dfrac{3}{4}x+3$
Work Step by Step
With an $x-$intercept of $
-4
$ and a $y-$intercept of $
3
$, the line passes through the points $(
-4,0
)$ and $(
0,3
).$
Using $y-y_1=\dfrac{y_1-y_2}{x_1-x_2}(x-x_1)$ or the Two-Point Form of linear equations, the equation of the line passing through $(
-4,0
)$ and $(
0,3
)$ is
\begin{array}{l}\require{cancel}
y-0=\dfrac{0-3}{-4-0}(x-(-4))
\\\\
y=\dfrac{0-3}{-4-0}(x+4)
\\\\
y=\dfrac{-3}{-4}(x+4)
\\\\
y=\dfrac{3}{4}(x+4)
\\\\
4\cdot y=4\cdot \dfrac{3}{4}(x+4)
\\\\
4y=3(x+4)
\\\\
4y=3x+12
\\\\
y=\dfrac{3}{4}x+\dfrac{12}{4}
\\\\
y=\dfrac{3}{4}x+3
.\end{array}
