Question

question 37 points 3

find the function which is parallel to \\(y = 2x + 9\\).

\\(5x - 2y = 8\\)

\\(7x + 2y = 14\\)

\\(4y - 8x = 24\\)

all of the choices

Explanation:

Identify the slope of the given line

The given equation is \(y = 2x + 9\).
Comparing this to the slope-intercept form \(y = mx + b\), the slope of the given line is:

$$m = 2$$

Parallel lines must have the same slope, so we are looking for an equation with a slope of \(2\).

Analyze the slope of each option

We rewrite each linear equation in slope-intercept form \(y = mx + b\) to find its slope:

1. For \(5x - 2y = 8\):

$$-2y = -5x + 8 \implies y = \frac{5}{2}x - 4 \implies m = \frac{5}{2}$$

1. For \(7x + 2y = 14\):

$$2y = -7x + 14 \implies y = -\frac{7}{2}x + 7 \implies m = -\frac{7}{2}$$

1. For \(4y - 8x = 24\):

$$4y = 8x + 24 \implies y = 2x + 6 \implies m = 2$$

Determine the parallel function

Since the line \(4y - 8x = 24\) has a slope of \(2\), which is equal to the slope of the given line \(y = 2x + 9\), it is parallel to the given line.

Answer:

• (A) \(5x - 2y = 8\)
• (B) \(7x + 2y = 14\)
• (C) \(4y - 8x = 24\) (Correct answer)
• (D) All of the choices