Question

The equation y = - 8) is graphed in the zy-plane. Which of the following equations will

have a graph that is parallel to the graph of the above equation and have an X-intercept on the
negative x-axis?

Answer 1

Listen to the other person not me!

Step-by-step explanation:

Answer 2

`y = (3)/(2)(x + 8)`

Step-by-step explanation:

Given

`y = (3)/(2)(x - 8)`

Required

Equation of line with the same slope and x intercept on negative axis

We start by solving for the slope of the first equation.

It should be noted that the slope of a line (in equation form) is the coefficient of x.

So, we start by opening the bracket of
`y = (3)/(2)(x - 8)`

This gives

`y = (3)/(2)(x) - (3)/(2)(8)`

`y = (3)/(2)(x) - (24)/(2)`

`y = (3)/(2)(x) - 12`

Hence, the slope of the line is
`(3)/(2)`

To solve for x intercept, we simply substitute 0 for y. This gives.

`0 = (3)/(2)(x) - 12`

Add 12 to both sides

`12 + 0 = (3)/(2)(x) - 12 + 12`

`12 = (3)/(2)(x)`

Multiply both sides by ⅔

`(2)/(3) * 12 = (3)/(2)(x) * (2)/(3)`

`(24)/(3) = (3)/(2)(x) * (2)/(3)`

`(24)/(3) = x`

`8 = x`

`x = 8`

This is the x intercept of equation
`y = (3)/(2)(x - 8)`

From the question we understand that the second equation has the same slope and has a negative x intercept as
`y = (3)/(2)(x - 8)`

For two parallel lines, their slope are always equal.

Hence, the second equation has the following info.

`Slope = (3)/(2)`

`x,intercept = -8`

This can be rewritten as follows;.

x = -8

Add 8 to both sides

x + 8 = -8 + 8

x + 8 = 0

Multiply both sides by the slope (3/2)

`(3)/(2)(x + 8) = (3)/(2) * 0`

`(3)/(2)(x + 8) = 0`

Recall that to solve for x intercept, we simply substitute 0 for y.

At this point, we also replace 0 with y.

This gives

`(3)/(2)(x + 8) = y`

`y = (3)/(2)(x + 8)`

Hence, the equation of the second line is
`y = (3)/(2)(x + 8)`