Question

1. the table below shows y, the number of questions micah answers correct on an answer sheet over time in days, x.

x	y
1	9
2	6

a) what is the rate of change of this relationship?
b) explain the meaning of the rate of change in context. what conclusions can you infer about micahs understanding of the content that week?

Explanation:

Step1: Recall rate - of - change formula

The rate of change formula for a linear relationship between two variables $x$ and $y$ is $\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Select two points from the table

Let's take the points $(x_1,y_1)=(0,12)$ and $(x_2,y_2)=(1,9)$.

Step3: Calculate the rate of change

$\frac{\Delta y}{\Delta x}=\frac{9 - 12}{1-0}=\frac{- 3}{1}=-3$.

The rate of change represents the number of questions Micah's correct answers decrease per day.

Answer:

A) The rate of change is - 3. This means that the number of questions Micah answers correctly on the answer sheet decreases by 3 each day. We can infer that Micah may be forgetting the content over time or getting more tired as the days progress, leading to a decline in the number of correct answers.