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

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.
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Answer 1

To compare the rates of change of the two linear functions, we need to determine their slopes.

Linear Function 1: \( y = x + 8 \)

• The slope (rate of change) of this function is 1, since the equation is in the form \( y = mx + b \), where \( m \) is the slope.

Linear Function 2:

• We have two points: \( (2, 6) \) and \( (4, 10) \). The slope can be calculated using the formula:

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

Substituting the points into the formula:

\[ \text{slope} = \frac{10 - 6}{4 - 2} = \frac{4}{2} = 2 \]

Now, we can compare the rates of change:

• Linear Function 1 has a slope of 1.
• Linear Function 2 has a slope of 2.

Since 2 (Linear Function 2) is greater than 1 (Linear Function 1), we conclude that:

Linear Function 2 has the greater rate of change.

So the answer is 2.