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

Using the Slope Formula and Linear Modeling knowledge points

$$
LATEXBLOCK0
$$

Calculate the slope

Using the Slope Formula knowledge point

$$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 0.5}{1 - 0} = 1.5 $$

Determine the y-intercept

Using the Linear Modeling knowledge point

$$ b = 0.5 $$

Write the linear function

Using the Linear Modeling knowledge point

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

Answer:

• \(f(x) = 0.5x + 1.5\)
• \(f(x) = 0.75x + 2\)
• \(f(x) = 1.5x + 0.5\) (Correct answer)
• \(f(x) = 2x + 0.75\)