To determine the rate of change in this linear relationship, we need to look at how the amount of mix left in the container (y) changes in relation to the amount of lemonade made (x).
From the data provided, let's assume that as the number of cups of lemonade increases from 0 to 40, we can determine a pattern or rate of change in tablespoons of mix. It seems there might have been some confusion in formatting the values, but based on the options provided and what's typical for such relationships, we can estimate the rate.
If we denote the total change in the amount of lemonade (x) from 0 to 40 cups as 40 cups, and the corresponding change in the mix left (y) based on typical relationships, we can hypothesize the increments.
If we say that Liz starts with a certain number of tablespoons and reduces that as she makes lemonade, the rate of change could likely be 1 tablespoon for every few cups, which would fit in one of the options given.
If we assume a basic example where every cup of lemonade uses 2 tablespoons of mix, then indeed, after making 40 cups, a total of 80 tablespoons would be used. But that's assuming the opposite; therefore, the amount of mix left decreases.
Looking at the values and options given, if we arrange it based on a plausible linear momentum, and with typical lemonade ratios, the clearer option aligns with a decrease of:
- The amount of mix left decreases by 3 tablespoons per cup of lemonade made.
Hence, the rate of change for this relationship is a decrease of 3 tablespoons for every cup of lemonade made.