Question

The slope of the function is

x: 1,2,3,4
y: 5.75, 11.50, 17.25, 23

The rate of change is measured in
The buyer spends at the rate of

Answer 1

To determine the slope of the function represented by the given points (x, y), we can calculate the slope (m) using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let's calculate the slope using the points provided. For every two consecutive points, we can compute the slope.

1. From (1, 5.75) to (2, 11.50):
\[
m_{1,2} = \frac{11.50 - 5.75}{2 - 1} = \frac{5.75}{1} = 5.75
\]

2. From (2, 11.50) to (3, 17.25):
\[
m_{2,3} = \frac{17.25 - 11.50}{3 - 2} = \frac{5.75}{1} = 5.75
\]

3. From (3, 17.25) to (4, 23):
\[
m_{3,4} = \frac{23 - 17.25}{4 - 3} = \frac{5.75}{1} = 5.75
\]

The slope between each of these points is a constant value of 5.75. Therefore, the overall slope of the function is 5.75.

### The Rate of Change
The rate of change in this context represents how much y changes for every unit increase in x. Here, it is 5.75, meaning that for each additional unit of x, y increases by 5.75.

### The Buyer Spends at the Rate of
Since the function suggests a relationship between x (which could represent the number of units sold or time, etc.) and y (which could represent monetary spending), we can infer that the buyer spends at the rate of $5.75 per unit of x.

So, in summary:
- The slope of the function is **5.75**.
- The rate of change is measured in **units of y per unit of x**.
- The buyer spends at the rate of **$5.75** per unit.