Question

A graph has time (years) on the x-axis and height (inches) on the y-axis. A line goes through points (2, 3) and (4, 6).

The graph shows a linear relationship between the height and years of a plant’s growth. Find the rate of change. Select all that apply.
The rate of change of a linear function is always the same.
The rate of change of a linear function increases as the input increases.
The rate of change from 2 years to 4 years on the graph is 1.5 inches per year.
The rate of change from 0 years to 6 years on the graph is 1.5 inches per year.

Answer 1

The rate of change of a linear function is always the same.

The rate of change from 2 years to 4 years on the graph is 1.5 inches per year.

The rate of change from 0 years to 6 years on the graph is 1.5 inches per year.

Explanation:

Slope = rate = (6 - 3)/(4 - 2) = 3/2

Slope of a straight line is constant hence the rate of change is also constant

Answer 2

A, C, and D

Explanation:

The rate of change will simply be the slope of the line, which we can find by taking the change in y and dividing that by the change in x:

slope =
`(6-3)/(4-2) =(3)/(2)`

Thus, the slope is 3/2 = 1.5.

Since the slope remains constant throughout the graph, we know that A is correct. In addition because the points 0, 2, 4, and 6 are on the graph, the rate of change between any of the two points will still be the constant 1.5, making C and D correct as well.

So, we can choose A, C, and D.

Hope this helps!