Answer
The point-slope form is $ y-5=3(x+2)$.
The slope-intercept form is $ y=3x+11$ or $ f(x)=3x+11$.
Work Step by Step
If the line passes through a point $(x_1,y_1)$ and slope is m, then point-slope form of the perpendicular line is.
$\Rightarrow y−y_1=m(x−x_1)$
From the question we have
$\Rightarrow (x_1,y_1)=(-2,5)$
Equation of the parallel line.
$\Rightarrow 3x-y=9$
Isolate $y$.
$\Rightarrow y=3x-9$
It is in the form of slope-intercept form $y=mx+c$.
The slope of the equation is $m=3$.
Two parallel lines have the same slopes.
The slope of the required line is
$\Rightarrow m_1=3$
Substitute all values into the point-slope equation.
$\Rightarrow y−5=(3)(x−(-2))$
Simplify.
$\Rightarrow y-5=3(x+2)$
The above equation is the point-slope form.
Now use the distributive property.
$\Rightarrow y-5=3x+6$
Add $5$ to both sides.
$\Rightarrow y-5+5=3x+6+5$
Simplify.
$\Rightarrow y=3x+11$
Let $y=f(x)$.
$\Rightarrow f(x)=3x+11$
The above equation is the slope-intercept form.
