Answer
The slope-intercept form of the line is $y=-2x+2$.
The graph of the line $y=-2x+2$ is:
Work Step by Step
The point-slope form of an equation of a line is $y-{{y}_{1}}=m\left( x-{{x}_{1}} \right)$.
Here, $m=-2$ , and $\left( {{x}_{1}},\,{{y}_{1}} \right)=\left( 3,\,-4 \right)$.
By substituting values of $m,\,{{x}_{1}}$ and ${{y}_{1}}$in $y-{{y}_{1}}=m\left( x-{{x}_{1}} \right)$, it gives
$y-\left( -4 \right)=-2\left( x-3 \right)$.
By simplifying,
$\Rightarrow y+4=-2x+6$.
$\Rightarrow y=-2x+6-4$.
$\Rightarrow y=-2x+6-4$.
$\Rightarrow y=-2x+2$.
So, the slope-intercept form of the line containing point $\left( 3,\,-4 \right)$ and having slope $-2$ is $y=-2x+2$.
