Question

Enter the equation of the line in slope-intercept form.

The line parallel to y =
7
4
x + 4 that passes through (−8, 0).

The equation of the line that passes through (−8, 0) is y = .

Answer 1

`y = (7)/(4)x +14`

Explanation:

Given

`y = (7)/(4)x + 4`

Required

Determine the equation of line that passes through (-8,0) and parallel to
`y = (7)/(4)x + 4`

Parallel lines have the same slope.

In
`y = (7)/(4)x + 4`

The slope, m is

`m = (7)/(4)`

because the general form of a linear equation is:

`y = mx + b`

Where

`m = slope`

So, by comparison:

`m = (7)/(4)`

Next, is to determine the equation of line through (-8,0)

This is calculated using:

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

Where

`m = (7)/(4)`

`(x_1,y_1) = (-8,0)`

So, we have:

`y - 0 = (7)/(4)(x -(-8))`

`y - 0 = (7)/(4)(x +8)`

`y - 0 = (7)/(4)x +(7)/(4)*8`

`y - 0 = (7)/(4)x +7*2`

`y - 0 = (7)/(4)x +14`

`y = (7)/(4)x +14`