Answer
Point-slope form $ y−0=-3(x+1)$.
Slope-intercept form $y=−3x−3$.
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
$\Rightarrow (x_1,y_1)=(-1,0)$
Equation of the parallel line.
$\Rightarrow 3x+y=6$
Isolate $y$.
$\Rightarrow y=-3x+6$
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
$\Rightarrow m=−3$
Substitute all values into the point-slope equation.
$\Rightarrow y−0=(-3)(x−(-1))$
Simplify.
$\Rightarrow y−0=-3(x+1)$
The above equation is the point-slope form.
Now use the distributive property.
$\Rightarrow y=-3x-3$
The above equation is the slope-intercept form.
