Question

Each line on this graph shows a constant rate of change. 1. What is the constant rate of change for Plant 2(the solid line in the middle.) 2. Explain what the constant rate of change means in the context of the situation.

Answer 1

The rate of change is also called the slope.

Thus, the rate of change of a line is also the slope of the same line.

To find the rate of change, apply the slope formula:

`m=(y2-y1)/(x2-x1)`

Question 1.

Rate of change for plant 2.

To find the rate of change for plant 2, take two points on the middle line.

(x1, y1) ==> (0, 1)

(x2, y2) ==> (4, 3.5)

Input the values into the formula:

`\begin{gathered} m=(3.5-1)/(4-0) \\ \\ m=(2.5)/(4) \\ \\ m=0.625 \end{gathered}`

Therefore, the rate of change for plant 2 is 0.625

Question 2.

A constant rate of change occurs when the value changes by the same amount during equal intervals.

The constant rate of change here means that the plant adds the same height each week. It can also be said that each plant grows at a constant rate every week.

ANSWER:

Question 1:

0.625

Question 2:

The constant rate of change here means the plant adds the same number of height each week (it grows at a constant rate every week).