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

Answer:

$y = \frac{3}{2}(x + 8)$

Explanation:

Given

$y = \frac{3}{2}(x - 8)$

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 $y = \frac{3}{2}(x - 8)$

This gives

$y = \frac{3}{2}(x) - \frac{3}{2}(8)$

$y = \frac{3}{2}(x) - \frac{24}{2}$

$y = \frac{3}{2}(x) - 12$

Hence, the slope of the line is $\frac{3}{2}$

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

$0 = \frac{3}{2}(x) - 12$

Add 12 to both sides

$12 + 0 = \frac{3}{2}(x) - 12 + 12$

$12 = \frac{3}{2}(x)$

Multiply both sides by ⅔

$\frac{2}{3} * 12 = \frac{3}{2}(x) * \frac{2}{3}$

$\frac{24}{3} = \frac{3}{2}(x) * \frac{2}{3}$

$\frac{24}{3} = x$

$8 = x$

$x = 8$

This is the x intercept of equation $y = \frac{3}{2}(x - 8)$

From the question we understand that the second equation has the same slope and has a negative x intercept as $y = \frac{3}{2}(x - 8)$

For two parallel lines, their slope are always equal.

Hence, the second equation has the following info.

$Slope = \frac{3}{2}$

$x,intercept = -8$

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)

$\frac{3}{2}(x + 8) = \frac{3}{2} * 0$

$\frac{3}{2}(x + 8) = 0$

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

At this point, we also replace 0 with y.

This gives

$\frac{3}{2}(x + 8) = y$

$y = \frac{3}{2}(x + 8)$

Hence, the equation of the second line is $y = \frac{3}{2}(x + 8)$

Answer 2

Answer:

Listen to the other person not me!

Explanation: