Question

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

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asked 2021-05-27

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.

Answers (1)

2021-05-28

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

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