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.

Question

Linear Function 1: y=x+8
y
=
x
+
8
Linear Function 2:
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.

(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 examine the slopes of both functions.

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

2. Linear Function 2: We can calculate the slope using the two given points: (2, 6) and (4, 10). The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the given 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.

Since 2 is greater than 1, Linear Function 2 has the greater rate of change.

Thus, the answer is: 2 (Linear Function 2 has a greater rate of change).