Question

Two different proportional relationships are represented by the equation and the table.
​Use the drop-down menus to complete the sentence comparing the rates of change of the proportional relationships.
​​
​The rate of change in Proportion A is

than the rate of change in proportion B.​

Answer 1

To complete the sentence comparing the rates of change of the proportional relationships, you will need to find the rates of change for both Proportion A and Proportion B based on their respective equations and the values in the table.

1. **Calculate the Rate of Change**:
- For Proportion A, if you have the equation or data points, calculate the rate of change (which is the slope in a linear relationship). This is usually found by taking two points \((x_1, y_1)\) and \((x_2, y_2)\) and using the formula:
\[
\text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1}
\]
- Repeat the same process for Proportion B.

2. **Compare the Rates**:
- If the rate for Proportion A is greater than Proportion B, you would fill in the blank with "greater".
- If it is less, you would use "less".
- If they are equal, you would use "equal".

So, depending on your calculations, the completed sentence could be:

- If A > B: "The rate of change in Proportion A is **greater** than the rate of change in Proportion B."
- If A < B: "The rate of change in Proportion A is **less** than the rate of change in Proportion B."
- If A = B: "The rate of change in Proportion A is **equal** to the rate of change in Proportion B."

Make sure to analyze the data accordingly to determine the correct relationship.