Question

(-4,-10/3),(-1,-4/3)

Determine the initial value and the rate of change of the linear function as given in the graph.

A. The initial value is 1/6. and the rate of change is 3/2

B. The initial value is -2/3, and the rate of change is 2/3

C. The initial value is 2/3, and the rate of change is -2/3

D. The initial value is -2, and the rate of change is 2/3

Answer 1

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

Let's start by finding the rate of change (m).

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

= (-(4/3) - (-10/3)) / (-1 - (-4))

= (-4/3 + 10/3) / (-1 + 4)

= (6/3) / 3

= 2/3

So, the rate of change is 2/3.

Now, let's find the initial value (b) by substituting the coordinates of one of the points in the slope-intercept form.

Using the point (-1, -4/3):

y = mx + b

-4/3 = (2/3)(-1) + b

-4/3 = -2/3 + b

b = -4/3 + 2/3

b = -2/3

Therefore, the initial value is -2/3.

The correct answer is B. The initial value is -2/3, and the rate of change is 2/3.