x,y

2,22
8,25
determine the rate of change and the initial value of the linear function given here as a table of values.

the rate of change is m= _ and the initial value is b=_

1 answer

To determine the rate of change, we can use the formula for finding the slope of a line passing through two points:

m = (y2 - y1) / (x2 - x1)

Using the points (2, 22) and (8, 25):

m = (25 - 22) / (8 - 2)
m = 3 / 6
m = 0.5

So, the rate of change (slope) is 0.5.

To find the initial value (y-intercept), we can substitute one of the points into the equation of a line and solve for the y-intercept. Let's use the point (2, 22):

y = mx + b
22 = 0.5(2) + b
22 = 1 + b
b = 22 - 1
b = 21

Therefore, the initial value (y-intercept) is 21.