Question

Compare Linear Function 1 with Linear Function 2. Which one has the greater rate of change? Choose 1 for Linear Function 1; choose 2 for Linear Function 2.

Linear Function 1: y=x+8
𝑦
=
𝑥
+
8
Linear Function 2:
<img alt="A coordinate plane shows the x-axis ranging from negative 2 to 6 in increments of 1 and the y-axis ranging from negative 2 to 12 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 2 comma 6 right parenthesis and left parenthesis 4 comma 10 right parenthesis. " height="800" src="
(1 point)
Linear Function has the greater rate of change.

Answer 1

To determine which linear function has a greater rate of change, we can analyze their slopes.

1. **Linear Function 1: \( y = x + 8 \)**
- The slope (rate of change) of this function is 1, since the coefficient of \( x \) is 1.

2. **Linear Function 2:**
- We need to find the slope using the two given points: (2, 6) and (4, 10).
- The slope (m) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
- Substituting in the points:
\[
m = \frac{10 - 6}{4 - 2} = \frac{4}{2} = 2
\]

Now, we can compare the slopes:
- **Linear Function 1** has a slope of 1.
- **Linear Function 2** has a slope of 2.

Thus, Linear Function 2 has the greater rate of change.

**Final Answer:** 2