Question

Determine the initial value and the rate of change of linear function is given in the graph on the answer to three decimal places as needed
X Y
-3 4
0 3
3 2
6 1

Answer 1

To determine the initial value (y-intercept) and the rate of change (slope) of the linear function, we can calculate the slope using two points from the graph.

First, let's choose two points from the graph: (-3, 4) and (0, 3).

The slope (rate of change) of a linear function is given by the formula:

slope = (change in y) / (change in x)

Using the points (-3, 4) and (0, 3):

slope = (3 - 4) / (0 - (-3))
slope = (-1) / (3)
slope = -1/3

Now that we have the slope, we can determine the initial value using one of the points. Let's use the point (0, 3) and the slope of -1/3 to find the initial value:

y = mx + b
3 = (-1/3)(0) + b
3 = b

Therefore, the initial value of the linear function is 3 and the rate of change is -1/3.