Answer
The equation of the line in point-slope form is $\left( y-2 \right)=2\left( x-4 \right)$ and slope-intercept form is
$y=2x-6$.
Work Step by Step
The slope of the line $y=2x$ is ${{m}_{1}}$ and slope of the line L is ${{m}_{2}}$.
From the graph it is clear that there are two lines that are parallel and the equation of one line is $y=2x$ and there is another parallel line passing through $\left( 4,2 \right)$.
Consider the equation $y=2x$.
The provided equation is in slope-intercept form. So, we compare the equation with the standard equation $y=mx+b$.
The slope of the equation $y=2x$ is $2$.
So, ${{m}_{1}}=2$
The slope of parallel lines are equal ${{m}_{1}}={{m}_{2}}$.
So, ${{m}_{2}}=2$
Label $\left( 4,2 \right)$ as $\left( {{x}_{1}},{{y}_{1}} \right)$and apply the point-slope formula:
$y-{{y}_{1}}=m\left( x-{{x}_{1}} \right)$
Substitute,
$\begin{align}
& {{x}_{1}}=4 \\
& {{y}_{1}}=2 \\
& \text{ }m=2
\end{align}$
The obtained equation is:
$y-2=2\left( x-4 \right)$
The point-slope form of the equation obtained is $y-2=2\left( x-4 \right)$.
Simplify the above equation to obtain the slope intercept form of the equation:
$\begin{align}
& y-2=2\left( x-4 \right) \\
& y-2=2x-8 \\
& y=2x-6
\end{align}$
The slope intercept form of the equation is $y=2x-6$ where the slope is $2$ and the y-intercept is $\left( 0,-6 \right)$.
