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.

Question

Linear Function 1: y=7x+4
y
=
7
x
+
4

Linear Function 2:
x
x
y
y

10 61
12 73
(1 point)

Answer 1

To determine which linear function has a lesser rate of change, we need to evaluate the slope of each function.

1. Linear Function 1: The function is given as \( y = 7x + 4 \). The rate of change (slope) is 7.

2. Linear Function 2: To find the slope of Linear Function 2, we can use the two points provided: (10, 61) and (12, 73). The slope \( m \) is calculated using the formula:

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

   Here, \( (x_1, y_1) = (10, 61) \) and \( (x_2, y_2) = (12, 73) \):

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

Now, we have the slopes:

• Slope of Linear Function 1: 7
• Slope of Linear Function 2: 6

Since 6 (the slope of Linear Function 2) is less than 7 (the slope of Linear Function 1), Linear Function 2 has the lesser rate of change.

Answer: 2