Question

a local public library decides to track the number of hours that a certain computer is being used. the table represents the number of hours, \\(y\\), which is dependent on the number of days, \\(x\\).

what is the linear equation that represents this situation?

\\(y = 8x + 45\\)
\\(y = 8x - 3\\)
\\(y = 2x + 16\\)
\\(y = 2x - 32\\)

Explanation:

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<reasoning>

Calculate the slope

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{37 - 21}{5 - 3} = \frac{16}{2} = 8
\]

Find the y-intercept

\[

$$\begin{aligned} y &= mx + b \\ 21 &= 8(3) + b \\ 21 &= 24 + b \\ b &= -3 \end{aligned}$$

\]

Write the linear equation

\[
y = 8x - 3
\]
</reasoning>

<answer>
<mcq-option>(A) \(y = 8x + 45\)</mcq-option>
<mcq-correct>(B) \(y = 8x - 3\)</mcq-correct>
<mcq-option>(C) \(y = 2x + 16\)</mcq-option>
<mcq-option>(D) \(y = 2x - 32\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Calculate the slope

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{37 - 21}{5 - 3} = \frac{16}{2} = 8
\]

Find the y-intercept

\[

$$\begin{aligned} y &= mx + b \\ 21 &= 8(3) + b \\ 21 &= 24 + b \\ b &= -3 \end{aligned}$$

\]

Write the linear equation

\[
y = 8x - 3
\]
</reasoning>

<answer>
<mcq-option>(A) \(y = 8x + 45\)</mcq-option>
<mcq-correct>(B) \(y = 8x - 3\)</mcq-correct>
<mcq-option>(C) \(y = 2x + 16\)</mcq-option>
<mcq-option>(D) \(y = 2x - 32\)</mcq-option>
</answer>

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