Question

use the graph to answer the question: (0.5,1), (0,0), (-1.5,-3).

determine the initial value and the rate of change of the linear function given in the graph

A) the initial value is 2, and the rate of change is 2
B) the initial value is 0, and the rate of change is 1/2
C) the initial value is -6, and the rate of change is 2
D) the initial value is 0, and the rate of change is 2

Answer 1

To determine the initial value and rate of change of the linear function from the given points, we can use the formula for the slope of a line, which is the rate of change, and solve for the initial value.

Using the points (0.5,1) and (0,0):
Rate of change = (y2 - y1) / (x2 - x1)
Rate of change = (1 - 0) / (0.5 - 0)
Rate of change = 1 / 0.5
Rate of change = 2

Now that we have found the rate of change, we can use one of the points to find the initial value. Let's use the point (0,0).

y = mx + b
0 = (2)(0) + b
0 = b

Therefore, the initial value is 0 and the rate of change is 2. So, the correct answer is:

D) the initial value is 0, and the rate of change is 2