Question

choose the correct option to complete each sentence. a swimming pool is filled with 120 gallons of water in 5 hours. which value is the x - value, and which is the y - value? what is the rate of change? the x - value is choose... 5 hours the y - value is choose... 120 gallons the rate of change is choose... 5 hours submit answer

Explanation:

Step1: Identify x and y values

In a rate - related context (like filling a pool), the independent variable (x - value) is usually the time, and the dependent variable (y - value) is the quantity (gallons of water). So the time of 5 hours is the x - value, and the number of gallons (120) is the y - value.

Step2: Calculate the rate of change

The rate of change (slope) is calculated as $\frac{y - y_1}{x - x_1}$. Here, if we consider the initial point as (0,0) and the final point as (5,120), the rate of change is $\frac{120 - 0}{5 - 0}=\frac{120}{5} = 24$ gallons per hour. But for the x - value, y - value part: x - value is 5 hours (time), y - value is 120 gallons (quantity of water). Then the rate of change is $\frac{120}{5}=24$ gallons per hour.

Answer:

The x - value is 5 hours, The y - value is 120 gallons, The rate of change is 24 gallons per hour (but for the given blanks: x - value: 5 hours, y - value: 120 gallons, and rate of change calculation gives 24, but if we follow the options where the rate is calculated as 120/5 = 24, but the blanks: x - value is 5 hours, y - value is 120 gallons, and the rate of change is 24 (but if the last blank is to be filled with 5 hours? No, wait the rate of change is 120/5 = 24. Wait the problem says "Choose the correct option to complete each sentence. A swimming pool is filled with 120 gallons of water in 5 hours. Which value is the x - value, and which is the y - value? What is the rate of change?" So x - value (independent variable, time) is 5 hours, y - value (dependent variable, gallons) is 120 gallons, rate of change is 120/5 = 24 gallons per hour. But the last blank has "5 hours" as an option? Wait maybe the rate of change is 120/5 = 24, but if the options for the rate of change are maybe 24, but the given options for the last blank is 5 hours? No, maybe I misread. Wait the user's image shows: "The x - value is 5 hours", "The y - value is Choose...", "The rate of change is 120 gallons" or "5 hours"? Wait no, let's re - examine. The x - value (time) is 5 hours, y - value (gallons) is 120 gallons, rate of change is 120/5 = 24. But if the options for y - value is 120 gallons, and rate of change is 24, but the last blank has "5 hours" as an option? Maybe there was a formatting error. But based on the standard rate of change (gallons per hour), it's 24. But if we follow the given options: x - value is 5 hours, y - value is 120 gallons, rate of change is 120/5 = 24, but if the last blank's option is 5 hours, that's incorrect. Wait maybe the problem is simpler: x is time (5 hours), y is gallons (120), rate is 120/5 = 24. But the user's image has "5 hours" as an option for the last blank. Maybe a mistake, but based on the context, x - value: 5 hours, y - value: 120 gallons, rate of change: 24 (but if we have to choose from the given options where the rate is 120/5 = 24, but the last blank has 5 hours, maybe the problem is structured as x - value (time) = 5 hours, y - value (gallons) = 120 gallons, rate of change = 120/5 = 24, but if the last blank is to be filled with 5 hours, that's wrong. Wait maybe the rate of change is 120/5 = 24, but the options are limited. Alternatively, maybe the rate of change is 24, but the given options for the last blank is 5 hours, which is incorrect. But following the standard:

x - value: 5 hours (time, independent variable)

y - value: 120 gallons (gallons, dependent variable)

rate of change: 120/5 = 24 gallons per hour.

But if the last blank has "5 hours" as an option, maybe it's a mistake, but based on the problem, the x - value is 5 hours, y - value is 120 gallons, and rate of change is 24. However, if we have to choose from the given options (as per the image: the last blank has "5 hours" as an option), maybe the problem is different. Wait the user's image:

"The x - value is 5 hours" (dropdown with 5 hours as option)

"The y - value is Choose..." (dropdown, likely 120 gallons)

"The rate of change is 120 gallons" or "5 hours"? No, rate of change is 120/5 = 24. But maybe the problem is considering the rate as 120 gallons over 5 hours, but the rate of change is 24. But given the options, maybe the x - value is 5 hours, y - value is 120 gallons, and the rate of change is 24 (but if the last blank is 5 hours, that's incorrect). Alternatively, maybe the rate of change is 120/5 = 24, but the options are not shown properly. But based on the standard, the answers are:

x - value: 5 hours

y - value: 120 gallons

rate of change: 24 gallons per hour.