Question

Write an equation for the line parallel to the given line that contains C.

Answer 1

Answer:

$y=-4x+15$

Step-by-step explanation:

step 1

Find the slope of the given line

we know that

If two lines are parallel, then their slopes are the same

The equation of the given line is

$y=-4x+1$

This is a equation of the line in slope intercept form

$y=mx+b$

where

m is the slope

b is the y-intercept

The slope m is equal to

$m=-4$

therefore

The slope of the line parallel to the given line is

$m=-4$

step 2

Find the equation in slope intercept form of the line parallel to the given line

$y=mx+b$

we have

$m=-4$

$point\ C(2,7)$

substitute the values and solve for b

$7=-4(2)+b$

$7=-8+b$

$b=7+8=15$

therefore

The linear equation is

$y=-4x+15$