Answer
Point-slope form $ y+5=4(x−3)$.
Slope-intercept form $y=4x−17$.
Work Step by Step
If the line passes through a point $(x_1,y_1)$ and slope is $m$, then the point-slope form of the perpendicular line's equation is.
$\Rightarrow y-y_1=m(x-x_1)$
From the question we have
$\Rightarrow (x_1,y_1)=(3,-5)$
Equation of the parallel line is $y=4x+7$
It is in the slope-intercept form $y=mx+c$.
Where, slope $m_1=4$.
The parallel lines have same slopes.
Hence, the slope of the required line is $m_2=4$
Substitute all values into the equation.
$\Rightarrow y-(-5)=4(x−3)$
Simplify.
$\Rightarrow y+5=4(x−3)$
The above equation is the point-slope form.
Now isolate y
$\Rightarrow y+5=4(x−3)$
Use distributive property.
$\Rightarrow y+5=4x−12$
Subtract $5$ from both sides.
$\Rightarrow y+5-5=4x−12-5$
Simplify.
$\Rightarrow y=4x−17$
The above equation is the slope-intercept form.
