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

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

1 answer

To determine the initial value and rate of change of a linear function, we can use the formula for the slope-intercept form of a linear function:

y = mx + b,

where m is the rate of change (the slope) and b is the initial value (the y-intercept).

First, let's find the rate of change (m). Rate of change is determined by the difference in y-coordinates divided by the difference in x-coordinates between two points on the graph.

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

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

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

m = (6/3) / (3)

m = 2/1

m = 2

Now, let's find the initial value (b) by substituting the coordinates of one of the points into the equation:

-4 = 2(-1) + b

-4 = -2 + b

b = -4 + 2

b = -2

Therefore, the initial value of the linear function is -2, and the rate of change is 2.