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 (graph with prism volume (cubic units) on y - axis from 1 to 10 and x - axis from 1 to 10, a blue line starting at the origin). what is the slope of the line? \\(\circ - 3\\) \\(\circ -\frac{1}{3}\\) \\(\circ \frac{1}{3}\\) \\(\circ 3\\)

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through the origin \((0,0)\) and another point, for example, when the pyramid volume (x - axis) is \(1\), the prism volume (y - axis) is \(3\), so the point is \((1,3)\). Another point is \((3,9)\) (when \(x = 3\), \(y=9\)).

Step2: Use the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(1,3)\). Then \(m=\frac{3 - 0}{1 - 0}=\frac{3}{1} = 3\). Or using \((0,0)\) and \((3,9)\), \(m=\frac{9 - 0}{3 - 0}=\frac{9}{3}=3\).

Answer:

3 (corresponding to the option "3")