# Use the given conditions to write an equation for the line in point-slope form a

Marvin Mccormick 2021-09-26 Answered

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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Yusuf Keller

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
$$\displaystyle{\left({x}_{{{1}}},{y}_{{{1}}}\right)}={\left(-{2},-{8}\right)}$$
Step 2
Using the formula of the equation of the line in
Slope intercept form
y=mx+c
point slope form
$$\displaystyle{\left({y}-{y}_{{{1}}}\right)}={m}{\left({x}-{x}_{{{1}}}\right)}$$
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
$$-8=-3(-2)+c$$
$$-8=6+c$$
$$\displaystyle\Rightarrow{c}=-{14}$$
So equation becomes
$$y=-3x-14$$
Step 4
Also, the equation of the line in point-slope form is given by
$$(y-(-8))=-3(x-(-2))$$
$$y+8=-3(x+2)$$