Question

x | y
2 | 22
5 | 25

determine the rate of change and initial values of the linear function given with a table of values.

Answer 1

To determine the rate of change and initial value of the linear function, we can use the formula for the rate of change (m) in a linear function:

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

Using the values from the table of values:

m = (25 - 22) / (5 - 2)
m = 3 / 3
m = 1

So, the rate of change of the linear function is 1.

To find the initial value (y-intercept) of the linear function, we can use the formula for the slope-intercept form of a linear function:

y = mx + b

Using the values from the table of values, we can substitute them into the equation and solve for the initial value (b):

22 = 1(2) + b
22 = 2 + b
b = 20

Therefore, the linear function can be written as:

y = x + 20