Determine the rate of change and the initial value of the linear function given x y

Question

2 22
8 25

Answer 1

To determine the rate of change and the initial value of the linear function, we need to find the slope and the y-intercept of the linear function.

First, find the slope using the given points (2, 22) and (8, 25):

Slope (m) = (y2 - y1) / (x2 - x1)
Slope (m) = (25 - 22) / (8 - 2)
Slope (m) = 3 / 6
Slope (m) = 0.5

Now that we have the slope, we can use one of the points to find the y-intercept. Let's use point (2, 22) in the point-slope form of a linear function:

y - y1 = m(x - x1)
y - 22 = 0.5(x - 2)
y - 22 = 0.5x - 1
y = 0.5x + 21

Therefore, the rate of change is 0.5 and the initial value is 21.