Question

kentish is arranging figurines on shelves. the number of figurines varies directly with the number of shelves. what is the constant of proportionality?
figurines
shelves

Explanation:

Step1: Recall direct variation formula

For direct variation, the formula is \( y = kx \), where \( y \) is the number of figurines, \( x \) is the number of shelves, and \( k \) is the constant of proportionality. We can solve for \( k \) as \( k=\frac{y}{x} \).

Step2: Use a point from the graph

Take the point \((1, 10)\) (when \( x = 1 \) shelf, \( y = 10 \) figurines). Substitute into \( k=\frac{y}{x} \): \( k=\frac{10}{1}=10 \). We can check with another point, e.g., \((2, 20)\): \( k=\frac{20}{2}=10 \), or \((3, 30)\): \( k=\frac{30}{3}=10 \), or \((4, 40)\): \( k=\frac{40}{4}=10 \). All give \( k = 10 \).

Answer:

10