Question

the graph shows the relationship between the volume of a rectangular prism and the volume of a square pyramid with an identical base and height.
prism vs. pyramid
what is the slope of the line?
-3
\frac{1}{3}
3
-\frac{1}{3}

Explanation:

Step1: Recall slope formula

The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify two points on the line

From the graph, we can see that when \( x = 1 \) (pyramid volume), \( y = 3 \) (prism volume), and when \( x = 0 \), \( y = 0 \). So we take the points \((0, 0)\) and \((1, 3)\).

Step3: Calculate the slope

Using the slope formula with \( x_1 = 0 \), \( y_1 = 0 \), \( x_2 = 1 \), \( y_2 = 3 \):
\( m=\frac{3 - 0}{1 - 0}=\frac{3}{1}=3 \)

Answer:

3