Question

Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (-5, -8): y = - 3x + 2​

Answer 1

Given:

The equation of line is

$y=-3x+2$

To find:

The equation of line parallel to given line and passes through (-5,-8).

Solution:

Slope intercept form of a line is

$y=mx+b$

where, m is slope and b is y-intercept.

On comparing the equation $y=-3x+2$ with the slope intercept form, we get

$m=-3$

Slope of given line is -3.

Slope of two parallel lines are same. So, the slope of parallel line is -3.

Equation of line passes thorough the point (-5,-8) with slope -3 is

$y-y_1=m(x-x_1)$

where, m is slope of the line.

$y-(-8)=-3(x-(-5))$

$y+8=-3(x+5)$

$y+8=-3x-15$

Subtract 8 from both sides.

$y=-3x-15-8$

$y=-3x-23$

Therefore, the equation of required line is $y=-3x-23$.