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:

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

$$ f(x) = 1.5x + 0.5 $$

Answer:

• (A) \(f(x) = 0.5x + 1.5\)
• (B) \(f(x) = 0.75x + 2\)
• (C) \(f(x) = 1.5x + 0.5\) (Correct answer)
• (D) \(f(x) = 2x + 0.75\)