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. A coordinate plane showing Prism versus Pyramid. The x-axis shows Pyramid Volume in cubic units and the y-axis shows Prism Volume in cubic units. The line starts at (0, 0) and passes through (1, 3), (2, 6) and (3, 9). What is the slope of the line?

Answer 1

The slope of the line is 3.

Explanation:

In the graph x-axis shows Pyramid Volume in cubic units and the y-axis shows Prism Volume in cubic units.

The line starts at (0, 0) and passes through (1, 3), (2, 6) and (3, 9).

If a line passes through two points
`(x_1,y_1)` and
`(x_2,y_2)`, then the slope of the line is

`m=(y_2-y_1)/(x_2-x_1)`

Consider any two points of the line: (0, 0) and (1, 3). So, the slope of the given line is

`m=(3-0)/(1-0)`

`m=3`

Therefore, the slope of the line is 3.

Answer 2

The slope of the line is 3

Explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
`y/x=k` or
`y=kx`

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem we have a line that passes through the origin,

so

The graph shows a proportional relation ship

`k=y/x`

For (1,3) ------>
`k=3/1=3`

For (2,6) ------>
`k=6/2=3`

For (3,9) ------>
`k=9/3=3`

The equation is

`y=3x`

The slope of the line is 3