#### Answer

$y=-2x+1$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the Point-Slope Form of linear equations to find the equation of the line with the following given characteristcs:
\begin{array}{l}\require{cancel}
\text{through }
(4,-7)
\text{ having slope }
-2
.\end{array}
Use the properties of equality to express the equation in the slope-intercept form.
$\bf{\text{Solution Details:}}$
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,
\begin{array}{l}\require{cancel}
y_1=-7
,\\x_1=4
,\\m=-2
,\end{array}
is
\begin{array}{l}\require{cancel}
y-(-7)=-2(x-4)
\\\\
y+7=-2(x-4)
.\end{array}
Using the properties of equality, in the form $y=mx+b$ or the Slope-Intercept Form, the equation above is equivalent to
\begin{array}{l}\require{cancel}
y+7=-2(x)-2(-4)
\\\\
y+7=-2x+8
\\\\
y=-2x+8-7
\\\\
y=-2x+1
.\end{array}