#### Answer

$\color{blue}{y+7=-2(x-4)}$

#### Work Step by Step

RECALL:
The point-slope form of a line's equation is $y-y_1=m(x-x_1)$ where $m$=slope and $(x_1, y_1)$ is a point on the line.
The given line has a slope of $-2$ and contains the point $(4, -7)$.
Substitute these into the point-slope form above to obtain:
$y-(-7) = -2(x-4)
\\\color{blue}{y+7=-2(x-4)}$