A graph has points (3, 9), (4, 13.5), and (5, 18).

Question

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.

Answer 1

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.