Answer
The equation of the line is $y=2x+7$.
Work Step by Step
The general slope–intercept form of the line having slope m is as follows:
$y-{{y}_{0}}=m\left( x-{{x}_{0}} \right)$
It is given that the line is passing through the point $\left( -3,1 \right)$. The slope of the line is the same as the line whose equation is $y=2x+1$. So the slope of the line is 2.
Now, substitute $\left( {{x}_{0}},{{y}_{0}} \right)=\left( -3,1 \right)$ and $m=2$ , that is,
$\begin{align}
& y-1=2\left( x+3 \right) \\
& y-1=2x+6 \\
& y=2x+6+1 \\
& y=2x+7
\end{align}$
Hence, the slope–intercept form of the line is $y=2x+7$.
