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: $y = x + 8$ • linear function 2: image of a graph with points (2,6) and (4,10)

Explanation:

Step1: Find rate of change for Linear Function 1

The equation of Linear Function 1 is \( y = x + 8 \). In the slope - intercept form \( y=mx + b \), where \( m \) is the slope (rate of change), the coefficient of \( x \) is 1. So the rate of change of Linear Function 1, \( m_1=1 \).

Step2: Find rate of change for Linear Function 2

For a linear function, the rate of change (slope) between two points \( (x_1,y_1) \) and \( (x_2,y_2) \) is given by the formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
We have two points for Linear Function 2: \( (2,6) \) and \( (4,10) \). Let \( x_1 = 2,y_1 = 6,x_2=4,y_2 = 10 \).
Then \( m_2=\frac{10 - 6}{4 - 2}=\frac{4}{2}=2 \).

Step3: Compare the two rates of change

We compare \( m_1 = 1 \) and \( m_2=2 \). Since \( 2>1 \), the rate of change of Linear Function 2 is greater than that of Linear Function 1.

Answer:

2