Question

Find an equation of the line through (1,8) and parallel to y = 4x + 8.y=(Type your answer in slope-intercept form.)

Answer 1

First of all, remember that parallel lines are those with equivalent slope. So, the given line is

`y=4x+8`

If the new line we have to find is parallel to this one, that means the slope is

`m=4`

Because the coefficient of x is always the slope.

Now, we know that the new line must pass through (1,8) and it must have a slope of 4. We can use the point-slope formula

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

Replacing the point and the slope, we have

`y-8=4(x-1)`

Then, we solve for y

`y=4x-4+8\rightarrow y=4x+4`

Therefore, the new parallel line is

`y=4x+4`