Question

Determine the rate of change and y-intercept

Answer 1

Rate of change = 12
y-intercept = (0, 20)

Step-by-step explanation:

Part 1) Rate of Change
The rate of change (or slope) is found using the formula
`m = (y_2 - y_1)/(x_2 - x_1)`.
To use this formula, we must take the coordinates of two of the given points in the table and substitute them. For simplicity, I'll take the points (1, 32) and (4, 68).

`m = (y_2 - y_1)/(x_2 - x_1) = (68 - 32)/(4 - 1) = \frac{36}3 = 12`

Therefore, the rate of change is 12.

Part 2) y-intercept
To find the y-intercept, we must find the value of the function where
`x = 0`. Since we have both the value of the function where
`x = 1` and we know that the rate of change is 12, we can simply subtract the rate of change from the y-value of the function at the point where
`x = 1`.

The y-value of the function where
`x = 1` is 32, therefore, the y-value of the function at
`x = 0` is
`32 - 12 = 20`

The y-intercept is (0, 20).

Answer 2

The slope of the line is 12

(Sorry for the bad quality image)

Step-by-step explanation:

To find the average rate of change, calculate the change in y over the change in x.

m = 12