Given:
The equation of line is [tex]y=-3x+7[/tex].
A line is parallel to given equation and passes through the point (-4,-8).
To find:
The equation of parallel line.
Solution:
The equation of a line is
[tex]y=-3x+7[/tex]
On comparing this equation with [tex]y=mx+b[/tex], we get
[tex]m=-3[/tex]
So, slope of given line is -3.
We know that, slopes of parallel lines are equal. It means, the slope of the parallel line is also -3.
The parallel line passes through (-4,-8) and having slope -3. So, the equation of line is
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-(-8)=(-3)(x-(-4))[/tex]
[tex]y+8=(-3)(x+4)[/tex]
[tex]y+8=-3x-12[/tex]
[tex]y=-3x-12-8[/tex]
[tex]y=-3x-20[/tex]
Therefore, the equation of parallel line is [tex]y=-3x-20[/tex].
