Question
A graph has points (3, 9), (4, 13.5), and (5, 18).
Given the graph of a linear function, identify the steps used to find the initial value. Check all that apply.
Find the rate of change using rise over run.
Find corresponding y values when x = 6, x = 7, and x = 8. Then plot the points to finish the line.
Find corresponding y values when x = 2, x = 1, and x = 0. Then plot the points to finish the line.
The initial value corresponds to the y value when x = 1.
The initial value corresponds to the y value when x = 0.
Given the graph of a linear function, identify the steps used to find the initial value. Check all that apply.
Find the rate of change using rise over run.
Find corresponding y values when x = 6, x = 7, and x = 8. Then plot the points to finish the line.
Find corresponding y values when x = 2, x = 1, and x = 0. Then plot the points to finish the line.
The initial value corresponds to the y value when x = 1.
The initial value corresponds to the y value when x = 0.
Answers
GPT-4o mini
To identify the initial value for a linear function based on the given points (3, 9), (4, 13.5), and (5, 18), here are the relevant steps:
1. **Find the rate of change using rise over run**: This step is indeed necessary for determining the slope (rate of change) of the linear function.
2. **Find corresponding y values when x = 6, x = 7, and x = 8. Then plot the points to finish the line.**: While this step helps extend the line, it's not directly needed to find the initial value.
3. **Find corresponding y values when x = 2, x = 1, and x = 0. Then plot the points to finish the line.**: This step is relevant as it allows you to find and identify the y-intercept (initial value) at x = 0.
4. **The initial value corresponds to the y value when x = 1.**: This is **not true**; the initial value is typically defined as the y-value when x = 0.
5. **The initial value corresponds to the y value when x = 0.**: This is **true**; it defines the y-intercept of the linear function.
In summary, the following steps apply:
- **Find the rate of change using rise over run.**
- **Find corresponding y values when x = 2, x = 1, and x = 0. Then plot the points to finish the line.**
- **The initial value corresponds to the y value when x = 0.**
1. **Find the rate of change using rise over run**: This step is indeed necessary for determining the slope (rate of change) of the linear function.
2. **Find corresponding y values when x = 6, x = 7, and x = 8. Then plot the points to finish the line.**: While this step helps extend the line, it's not directly needed to find the initial value.
3. **Find corresponding y values when x = 2, x = 1, and x = 0. Then plot the points to finish the line.**: This step is relevant as it allows you to find and identify the y-intercept (initial value) at x = 0.
4. **The initial value corresponds to the y value when x = 1.**: This is **not true**; the initial value is typically defined as the y-value when x = 0.
5. **The initial value corresponds to the y value when x = 0.**: This is **true**; it defines the y-intercept of the linear function.
In summary, the following steps apply:
- **Find the rate of change using rise over run.**
- **Find corresponding y values when x = 2, x = 1, and x = 0. Then plot the points to finish the line.**
- **The initial value corresponds to the y value when x = 0.**