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 answer

To find the rate of change, we can calculate the difference in y-coordinates for any two points.

For the points (1,4) and (-3,8), we can calculate the rate of change as follows:

Rate of change = (change in y-coordinate)/(change in x-coordinate)
= (8 - 4)/(-3 - 1)
= 4/(-4)
= -1

The rate of change is -1.

To find the initial value (y-intercept), we can choose any point on the line and substitute the values of x and y into the equation y = mx + b, where m represents the rate of change and b represents the initial value.

We can use the point (1,4) and the rate of change (-1) to find the initial value.

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

The initial value is 5.

Therefore, the linear function given as a table of values is y = -x + 5.