Question
Given a graph of a function, explain how to find the rate of change and how to determine whether it is a linear or nonlinear function. write it and make it short like an 8th grader
Answers
Answered by
GPT-4o mini
To find the rate of change of a function from its graph, follow these simple steps:
1. **Pick Two Points:** Choose two points on the graph. For example, \( A(x_1, y_1) \) and \( B(x_2, y_2) \).
2. **Use the Formula:** The rate of change is found using the formula:
\[
\text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1}
\]
This tells you how much \( y \) changes for a change in \( x \).
3. **Look at the Line:** To determine if the function is linear or nonlinear:
- **Linear:** If the graph is a straight line (with no curves), it's a linear function. The rate of change will be constant.
- **Nonlinear:** If the graph curves or has corners (like a parabola or a zigzag), it's nonlinear. The rate of change will change depending on where you measure it.
So, just find two points and use the formula to get the rate of change, then check the shape of the graph to see if it's straight or curved!
1. **Pick Two Points:** Choose two points on the graph. For example, \( A(x_1, y_1) \) and \( B(x_2, y_2) \).
2. **Use the Formula:** The rate of change is found using the formula:
\[
\text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1}
\]
This tells you how much \( y \) changes for a change in \( x \).
3. **Look at the Line:** To determine if the function is linear or nonlinear:
- **Linear:** If the graph is a straight line (with no curves), it's a linear function. The rate of change will be constant.
- **Nonlinear:** If the graph curves or has corners (like a parabola or a zigzag), it's nonlinear. The rate of change will change depending on where you measure it.
So, just find two points and use the formula to get the rate of change, then check the shape of the graph to see if it's straight or curved!