Question

Use the table to answer the question.

x y
1 4
−3 8
Find the rate of change and the initial value of the linear function given as a table of values.

(1 point)
The rate of change is m=
, and the initial value is b=

Answer 1

To find the rate of change of the linear function, we need to calculate the slope between two points. We can choose any two points from the table. Let's choose the points (1, 4) and (-3, 8).

The formula for calculating the slope between two points (x1, y1) and (x2, y2) is:

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

Using the points (1, 4) and (-3, 8), we can plug in the values into the formula:

m = (8 - 4) / (-3 - 1)
m = 4 / (-4)
m = -1

Therefore, the rate of change (slope) of the linear function is -1.

To find the initial value (y-intercept) of the linear function, we can use any point from the table. Let's choose the point (1, 4).

The equation of a linear function is in the form y = mx + b, where m is the slope and b is the y-intercept.

We know that the slope is -1. Using the point (1, 4), we can substitute the x and y values into the equation and solve for b:

4 = -1(1) + b
4 = -1 + b
b = 4 + 1
b = 5

Therefore, the initial value (y-intercept) of the linear function is 5.