Question
A student is completing a homework assignment. Each minute the student records the number of problems left to complete. The table shows the data. What is the rate of change of this linear function? What does the rate of change represent in this situation?
Homework Assignment
Time (minutes)
0
1
2
3
4
5
Problems Left
17
14
11
8
5
2
Question content area bottom
Part 1
What is the rate of change of this linear function?
The rate of change is
enter your response here.
Homework Assignment
Time (minutes)
0
1
2
3
4
5
Problems Left
17
14
11
8
5
2
Question content area bottom
Part 1
What is the rate of change of this linear function?
The rate of change is
enter your response here.
Answers
GPT-4o mini
To determine the rate of change of the linear function represented by the homework assignment data, we need to examine how the number of problems left changes over time.
From the provided data:
```
Time (minutes): 0 1 2 3 4 5
Problems Left: 17 14 11 8 5 2
```
We can calculate the rate of change by examining two points from the table. Let's take the points (0, 17) and (5, 2).
The formula for the rate of change (slope) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
\text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in the values:
- \(x_1 = 0\), \(y_1 = 17\)
- \(x_2 = 5\), \(y_2 = 2\)
We get:
\[
\text{Rate of Change} = \frac{2 - 17}{5 - 0} = \frac{-15}{5} = -3
\]
Thus, the rate of change of this linear function is -3.
### Interpretation:
The rate of change of -3 means that the student is completing 3 problems every minute. The negative sign indicates that the number of problems left is decreasing as time progresses.
From the provided data:
```
Time (minutes): 0 1 2 3 4 5
Problems Left: 17 14 11 8 5 2
```
We can calculate the rate of change by examining two points from the table. Let's take the points (0, 17) and (5, 2).
The formula for the rate of change (slope) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
\text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in the values:
- \(x_1 = 0\), \(y_1 = 17\)
- \(x_2 = 5\), \(y_2 = 2\)
We get:
\[
\text{Rate of Change} = \frac{2 - 17}{5 - 0} = \frac{-15}{5} = -3
\]
Thus, the rate of change of this linear function is -3.
### Interpretation:
The rate of change of -3 means that the student is completing 3 problems every minute. The negative sign indicates that the number of problems left is decreasing as time progresses.