To determine which function shows a fabric with a price of \[tex]$1.25 per square yard, we can analyze the given data in the table and calculate the slope, which represents the price per square yard.
We'll solve this step by step using the information provided:
1. Understanding the Table:
- The table shows the relationship between the number of square yards of fabric and its corresponding price.
- Specifically, for:
- 1 square yard, the price is \$[/tex]1.25
- 2 square yards, the price is \[tex]$2.00
- 3 square yards, the price is \$[/tex]2.75
- 4 square yards, the price is \[tex]$3.50
2. Interpreting the Relationship:
- We want to find an equation that represents the price (y) as a function of the number of square yards (x).
3. Calculating the Slope:
- The slope (m) of the line can be determined by taking the change in the price divided by the change in the number of square yards.
4. Using Two Data Points:
- We can use any two data points from the table. Let's use (1, 1.25) and (2, 2.00).
- The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
5. Substituting the Values:
- Here, \( (x_1, y_1) = (1, 1.25) \) and \( (x_2, y_2) = (2, 2.00) \):
\[
m = \frac{2.00 - 1.25}{2 - 1} = \frac{0.75}{1} = 0.75
\]
6. Conclusion:
- The slope of the line is 0.75, which means the price per square yard of the fabric is \$[/tex]0.75.
Therefore, the function shows that the fabric has a price of \$0.75 per square yard. The detailed step-by-step calculation illustrates how we arrived at this conclusion by using the slope formula between the given data points.
