Question

the graph shows the relationship between the weight of a box and the number of books added to the box. what function represents the weight of a box based on \\(x\\), the number of books?

\\(f(x) = 0.5x + 1.5\\)
\\(f(x) = 0.75x + 2\\)
\\(f(x) = 1.5x + 0.5\\)
\\(f(x) = 2x + 0.75\\)

Explanation:

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<reasoning>

Identify points from the graph

\[
(0, 0.5), \quad (1, 2), \quad (2, 3.5), \quad (3, 5), \quad (4, 6.5), \quad (5, 8), \quad (6, 9.5)
\]

Determine the y-intercept

\[
b = 0.5
\]

Calculate the slope

\[
m = \frac{2 - 0.5}{1 - 0} = 1.5
\]

Formulate the linear function

\[
f(x) = 1.5x + 0.5
\]
</reasoning>

<answer>
<mcq-option>(A) \(f(x) = 0.5x + 1.5\)</mcq-option>
<mcq-option>(B) \(f(x) = 0.75x + 2\)</mcq-option>
<mcq-correct>(C) \(f(x) = 1.5x + 0.5\)</mcq-correct>
<mcq-option>(D) \(f(x) = 2x + 0.75\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify points from the graph

\[
(0, 0.5), \quad (1, 2), \quad (2, 3.5), \quad (3, 5), \quad (4, 6.5), \quad (5, 8), \quad (6, 9.5)
\]

Determine the y-intercept

\[
b = 0.5
\]

Calculate the slope

\[
m = \frac{2 - 0.5}{1 - 0} = 1.5
\]

Formulate the linear function

\[
f(x) = 1.5x + 0.5
\]
</reasoning>

<answer>
<mcq-option>(A) \(f(x) = 0.5x + 1.5\)</mcq-option>
<mcq-option>(B) \(f(x) = 0.75x + 2\)</mcq-option>
<mcq-correct>(C) \(f(x) = 1.5x + 0.5\)</mcq-correct>
<mcq-option>(D) \(f(x) = 2x + 0.75\)</mcq-option>
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