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:

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<reasoning>

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.
</reasoning>

<answer>
<mcq-option>(A) \(5x - 2y = 8\)</mcq-option>
<mcq-option>(B) \(7x + 2y = 14\)</mcq-option>
<mcq-correct>(C) \(4y - 8x = 24\)</mcq-correct>
<mcq-option>(D) All of the choices</mcq-option>
</answer>

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Answer:

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<reasoning>

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.
</reasoning>

<answer>
<mcq-option>(A) \(5x - 2y = 8\)</mcq-option>
<mcq-option>(B) \(7x + 2y = 14\)</mcq-option>
<mcq-correct>(C) \(4y - 8x = 24\)</mcq-correct>
<mcq-option>(D) All of the choices</mcq-option>
</answer>

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