Step 1

To find the equation of a line which is parallel to the line whose equation is \(y=-3x+4\). Since we know that the parallel lines have the same slope so the value of the slope of the required line is -3 that is

\(m=-3\)

Also the given point is

\((x_{1},y_{1})=(-2,-8)\)

Step 2

Using the formula of the equation of the line in

Slope intercept form

\(y=mx+c\)

point slope form

\((y-y_{1})=m(x-x_{1})\)

Step 3

The equation of the line in slope-intercept form is given by

\(y=-3x+c\)

Since line is passing through (-2,-8) so

\(-8=-3(-2)+c\)

\(-8=6+c\)

\(\Rightarrow c=-14\)

So equation becomes

\(y=-3x-14\)

Step 4

Also, the equation of the line in point-slope form is given by

\((y-(-8))=-3(x-(-2))\)

\(y+8=-3(x+2)\)