Answer
$y=2x+5$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the Two-Point form of linear equations to find the equation of the line with the given characteristics:
\begin{array}{l}\require{cancel}
\text{contains }
(-4,-3)
\text{ and }
(-1,3)
.\end{array}
Then use the properties of equality to convert the equation to Slope-Intercept form.
$\bf{\text{Solution Details:}}$
Using $y-y_1=\dfrac{y_1-y_2}{x_1-x_2}(x-x_1)$ or the Two-Point Form of linear equations, where
\begin{array}{l}\require{cancel}
x_1=-4
,\\x_2=-1
,\\y_1=-3
,\\y_2=3
,\end{array}
the equation of the line is
\begin{array}{l}\require{cancel}
y-y_1=\dfrac{y_1-y_2}{x_1-x_2}(x-x_1)
\\\\
y-(-3)=\dfrac{-3-3}{-4-(-1)}(x-(-4))
\\\\
y+3=\dfrac{-3-3}{-4+1}(x+4)
\\\\
y+3=\dfrac{-6}{-3}(x+4)
\\\\
y+3=2(x+4)
.\end{array}
Using the properties of equality, in $y=mx+b$ or the Slope-Intercept form, the equation above is equivalent to
\begin{array}{l}\require{cancel}
y+3=2(x+4)
\\\\
y+3=2(x)+2(4)
\\\\
y+3=2x+8
\\\\
y=2x+8-3
\\\\
y=2x+5
.\end{array}
