Question

Compare linear function 1 with linear function 2 which one had the greater rate of change
X. Y
5. 26
13. 34

Answer 1

To compare the rates of change (slopes) of two linear functions, we first need to identify their respective slopes using the given points.

Let's denote the two functions as follows:

- **Linear Function 1**: Uses the points \( (5, 26) \) and \( (13, 34) \)

We can calculate the slope (rate of change) using the formula:

\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]

For **Linear Function 1**:

- \( (x_1, y_1) = (5, 26) \)
- \( (x_2, y_2) = (13, 34) \)

Substituting these values into the slope formula:

\[
\text{slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1
\]

Now, you referenced **Linear Function 2**, but didn’t provide any additional points. Hence, I can only compare the calculated slope of **Linear Function 1** which is 1.

If you provide similar points for **Linear Function 2**, we would apply the same method to calculate its rate of change, and then we could compare the two. Please provide the additional data for **Linear Function 2** so we can continue.