Question

Ramonas's lemonade pitcher holds 32 ounces of lemonade but has a crack and leaks lemonade at a rate of 3 ounces per minute.

Graph the situation
1. What is the x-intercept and what does it mean?
2. What is the rate of change and what does it represent?
3. What is the y-intercept and what does it represent?

Answer 1

Please find the graph of the situation created with MS Excel

1. The duration after which the pitcher will be empty, which is 10.67 minutes

2. The rate, -3 ounces per minute, represents the rate at which the lemonade leaks from the pitcher

3. The y-intercept is 32, which represents the initial amount of lemonade in the pitcher

The amount of lemonade in the pitcher can be found as follows;

The situation can be represented by a linear equation, where the y-axis represents the amount of lemonade in the pitcher (in ounces), and the x-axis represents time (in minutes).

1. X-Intercept: The x-intercept is the point where the line crosses the x-axis. This represents the time at which the pitcher will be empty. Since the pitcher initially holds 32 ounces and leaks at a rate of 3 ounces per minute, it will be empty after
`(32)/(3) \approx 10.67` minutes. So, the x-intercept is approximately 10.67, which means the pitcher will be empty after about 10.67 minutes.

2. Rate of Change: The rate of change of a function is the slope of the line. In this case, the rate of change is -3, which represents the rate at which the pitcher is losing lemonade, or 3 ounces per minute.

3. Y-Intercept: The y-intercept is the point where the line crosses the y-axis. This represents the initial amount of lemonade in the pitcher before any has leaked out. In this case, the y-intercept is 32, which means the pitcher initially held 32 ounces of lemonade.