# Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Passing through (-2,-8) and parallel to the line whose equation is y=-3x+4

Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form.
Passing through (-2,-8) and parallel to the line whose equation is $$y=-3x+4$$
Write an equation for the line in point-slope form and slope-intercept form.

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