Answer
Point-slope form: $ y+7=-3(x-4)$.
Slope-intercept form: $y=-3x+5$.
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 line's equation is.
$\Rightarrow y-y_1=m(x-x_1)$
We are given
$\Rightarrow (x_1,y_1)=(4,-7)$
The slope $m$ of the required line is equal to the slope $m_1$ of the line $3x+y=9$ because the two lines are parallel.
We bring the equation of the line $3x+y=9$ to the slope-intercept form $y=mx+c$:
Isolate $y$.
$y=-3x+9$
Identify its slope:
$m_1=-3$.
Since $m=m_1=-3$ and $(x_1,y_1)=(4,-7)$, we can write the equation of the required line:
$\Rightarrow y-(-7)=(-3)(x-(4))$
Simplify.
$\Rightarrow y+7=-3(x-4)$
The above equation is the point-slope form.
Now isolate $y$.
Use the distributive property.
$\Rightarrow y+7=-3x+12$
Subtract $7$ from both sides.
$\Rightarrow y+7-7=-3x+12-7$
Simplify.
$\Rightarrow y=-3x+5$
The above equation is the slope-intercept form.
