Question

Question

Compare Linear Function 1 with Linear Function 2. Which one has the lesser rate of change? Choose 1 for Linear Function 1; choose 2 for Linear Function 2.
Linear Function 1: y=7x+4

Linear Function 2:
x
y

10 61
12 73
(1 point)
Linear Function
has the lesser rate of change.
Remaining Attempts : 3

Answer 1

To determine which of the two linear functions has the lesser rate of change, we need to analyze each function.

Linear Function 1: Given in slope-intercept form \( y = 7x + 4 \). The rate of change (slope) here is 7.

Linear Function 2: We can find the slope of this function using the points provided. 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 points \( (10, 61) \) and \( (12, 73) \):

\[ m = \frac{73 - 61}{12 - 10} = \frac{12}{2} = 6 \]

Now, we compare the slopes of the two functions:

• Linear Function 1 has a rate of change of 7.
• Linear Function 2 has a rate of change of 6.

Since 6 is less than 7, Linear Function 2 has the lesser rate of change.

Thus, the answer is:

2 (for Linear Function 2).