Question

the number of place settings of dishes varies directly with the number of boxes. how many place settings are in each box?
place settings
boxes
your answer

Explanation:

Step1: Identify a point on the graph

From the graph, when the number of boxes (x) is 1, the number of place settings (y) is 4. When x = 2, y = 8; when x = 3, y = 12.

Step2: Calculate the ratio (constant of proportionality)

For direct variation, \( y = kx \), so \( k=\frac{y}{x} \). Using the point (1, 4), \( k = \frac{4}{1}=4 \). Checking with (2, 8): \( \frac{8}{2}=4 \), and (3, 12): \( \frac{12}{3}=4 \). So the constant of proportionality (number of place settings per box) is 4.

Answer:

4