Determine if the given graph of the function y= -2/5x + 3. Enter 1 for yes. Enter 2 for no (1 point)

Answer 1

(1) Yes

Answer 2

Use the table to answer the question

X Y
2 22
8 25

Determine the rate of change and the initial value of the linear function given here as a table of values. (1 point)

The rate of change is m= , and the initial value is b= .

Answer 3

To determine the rate of change, we use the formula:

m = (Y2 - Y1) / (X2 - X1)

Using the given values from the table:

m = (25 - 22) / (8 - 2)
m = 3 / 6
m = 1/2

The rate of change is 1/2.

To determine the initial value, we can choose any point from the table. Let's use the point (2, 22). The initial value is the value of y when x is 0.

So, b = y - mx = 22 - (1/2) * 2
b = 22 - 1
b = 21

The initial value is 21.

Therefore, the rate of change is m = 1/2 and the initial value is b = 21.

Answer 4

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: (4, 10) , (2, 6)

Linear Function has the greater rate of change

Answer 5

To compare the rate of change of Linear Function 1 and Linear Function 2, we need to find the slope (rate of change) of each function.

For Linear Function 1, the slope is equal to the coefficient of x, which is 1. So, the rate of change for Linear Function 1 is 1.

For Linear Function 2, we can use the formula:

m = (Y2 - Y1) / (X2 - X1)

Using the given values (4, 10) and (2, 6):

m = (6 - 10) / (2 - 4)
m = -4 / -2
m = 2

The rate of change for Linear Function 2 is 2.

Therefore, Linear Function 2 has the greater rate of change.