Question

Determine the initial value and the rate of change of the linear function given in the graph. (1 point)

(0,0) (2,3)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine the initial value of the linear function, we look at the y-intercept, which is the point where the line crosses the y-axis. In this case, the y-intercept is the point (0,0), so the initial value is 0.

To determine the rate of change of the linear function, we calculate the slope of the line. The slope is the change in y divided by the change in x between two points on the line. In this case, we can use the points (0,0) and (2,3) to calculate the slope:

Slope = (change in y) / (change in x)
Slope = (3 - 0) / (2 - 0)
Slope = 3 / 2
Slope = 1.5

Therefore, the initial value of the linear function is 0 and the rate of change is 1.5.

Answer 2

Determine the initial value and the rate of change of the linear function as given in the graph. (1 point)

(-3,2.5) (0,1) (2,0)

Answer 3

[AI-generated answer — Bot GPT 3.5]

To determine the initial value and the rate of change of the linear function, we can use the given points on the graph: (-3, 2.5), (0, 1), and (2, 0).

First, we can calculate the rate of change (slope) of the linear function using the points (0,1) and (2, 0):

Slope = (change in y) / (change in x)
Slope = (0 - 1) / (2 - 0)
Slope = -1 / 2
Slope = -0.5

Now, we can use the slope to find the initial value of the function. Let's use the point (0,1) to calculate the initial value:

y = mx + b
1 = (-0.5)(0) + b
1 = b

Therefore, the initial value of the linear function is 1 and the rate of change is -0.5.