Question

Determine the initial value and the rate of change of the linear function as given in the graph 1.1, -4/3 last point negative 4, -10/3

Answer 1

To determine the initial value and rate of change of the linear function, we can use the two points (-4, -10/3) and (1, -4/3) from the graph.

First, let's calculate the rate of change, which represents the slope of the line:
Rate of Change = (Change in y) / (Change in x) = (-4/3 - (-10/3)) / (1 - (-4)) = (6/3) / 5 = 2/5

Therefore, the rate of change of the linear function is 2/5.

Next, let's find the initial value of the linear function. We can pick one of the points and use the rate of change to find the y-intercept.

Using the point (-4, -10/3) and the rate of change of 2/5:
-10/3 = (2/5)(-4) + b
-10/3 = -8/5 + b
b = -10/3 + 8/5
b = -50/15 + 24/15
b = -26/15

Therefore, the initial value of the linear function is -26/15.