Question

according to the graph, what is the value of the constant in the equation below?
height = \frac{constant}{width}
(the graph shows a curve with points (3, 25), (5, 15), (15, 5), (25, 3))
options:
a. 75
b. 3
c. 25
d. 15

Explanation:

Step1: Recall the equation

The equation is \( \text{Height} = \frac{\text{Constant}}{\text{Width}} \), which can be rearranged to \( \text{Constant} = \text{Height} \times \text{Width} \).

Step2: Use a point from the graph

Let's take the point \( (3, 25) \) where Width = 3 and Height = 25. Substitute into the rearranged equation: \( \text{Constant} = 25 \times 3 \).

Step3: Calculate the constant

\( 25 \times 3 = 75 \). We can verify with another point, e.g., \( (5, 15) \): \( 15 \times 5 = 75 \), \( (15, 5) \): \( 5 \times 15 = 75 \), \( (25, 3) \): \( 3 \times 25 = 75 \). All give the same constant.

Answer:

A. 75