Question

A line is parallel to y = 2x – 8 and

intersects the point (-4, -1). What is the
equation of this parallel line?
y = [?]x + [ ]
Hint: Use the Point-Slope Form: y - y1 = m(x - X1)
Then write the equation in slope-intercept form.

Answer 1

y = 2x + 7

Explanation:

y - y1 = m(x - x1)

First, put y and x into the equation and enter the slope, which is 2.

y + 1 = 2(x + 4)

(The negative 1 and 4 are changed to a positive 1 and 4 since the two negative signs cancel each other out)

Next, distribute.

y + 1 = 2x + 8

Then, you move the 1 to the other side of the equation to isolate the y. This will change the 1's sign into a negative and you will result with this after adding like terms:

y = 2x + 7

The equation of the line parallel to y = 2x - 8, and that goes through the point (-4, -1) is y = 2x + 7

Answer 2

y=2x+7

Explanation:

When an equation is parallel to another, it shares the same slope.

Our original line is y=2x-8, and it is in slope-intercept form (y=mx+b)

This means that our slope is 2 because m represents the slope.

The slope of our parallel line will then also be 2.

We can begin to plug that into point-slope form which is:

y - y1 = m(x - x1)

This is where (x1, y1) is a point the line intersects, and m is the slope.

Plugging in the slope, we'll have:

y - y1 = 2(x - x1)

We also know it intersects the point (-4, -1）

We can plug this into our equation as well.

y - (-1) = m(x - (-4))

y+1=2(x+4)

Now, we can simplify it into slope-intercept form:

y+1=2(x+4)

Distribute

y+1=2x+8

Subtract 1 from both sides

y=2x+8-1

y=2x+7