Determine the initial value and the rate of change of the linear function as given in the graph. the points on the graph are (0,0), (0.5, 1), and(-1.5, -3) (1 point)

Question

The initial value is −6, and the rate of change is 2.
The initial value is 2, and the rate of change is 2.
The initial value is 0, and the rate of change is 2.
The initial value is 0, and the rate of change is 1/2.

Answer 1

To determine the initial value and rate of change of the linear function, we can use the formula for the equation of a line: y = mx + b, where m is the rate of change (slope) and b is the initial value (y-intercept).

Given the points (0,0), (0.5, 1), and (-1.5, -3), we can find the slope (rate of change) using the formula:

m = (y2 - y1) / (x2 - x1)

Using the points (0,0) and (0.5,1):
m = (1 - 0) / (0.5 - 0)
m = 1 / 0.5
m = 2

So, the rate of change is 2.

To find the initial value (y-intercept), we can substitute any of the given points into the equation y = mx + b and solve for b.

Using the point (0, 0):
0 = 2(0) + b
0 = b

Therefore, the initial value is 0.

Hence, the correct answer is:

- The initial value is 0, and the rate of change is 2.

Answer 2

correct?

Answer 3

Apologies for the mistake in my previous response. That answer is incorrect.

Let's re-evaluate the given points to determine the correct initial value and rate of change.

Given points: (0,0), (0.5, 1), and (-1.5, -3)

To find the rate of change (slope), we can use the formula:

m = (y2 - y1) / (x2 - x1)

Using the points (0,0) and (0.5, 1):
m = (1 - 0) / (0.5 - 0)
m = 1 / 0.5
m = 2

So, the rate of change is 2.

Now, let's use one of the given points (0,0) and substitute it into the equation y = mx + b to find the initial value (y-intercept).

0 = 2(0) + b
0 = 0 + b
b = 0

Therefore, the initial value is 0.

So, the correct answer is:

- The initial value is 0, and the rate of change is 2.