A trainer for a professional football team keeps track of the amount of water players consume throughout practice. The trainer observes that the amount of water consumed is a liner function of the temperature on a given day. The trainer finds that when it is 90 degrees, the players consume about 220 gallons of water and when it is 76 degrees the players consumer about 178 gallons of water.
Part A: Write a linear function to model the relationship between the gallons of water consumed and the temperature
Part B: Explain the meaning of the slope in the context of the problem.
(90, 220) and (76, 178)
You have two points, so you can write an equation of a straight line in the form or y = mx + b
First find the slope: m =(220-178)/(90-76)
Once you have the slope. Use it and one of the points to find the equation of the line.
To interpret the slope the numerator represents the gallons of water/per degree.
78 euros
42
142
Part A: To write a linear function to model the relationship between the gallons of water consumed and the temperature, we need to determine the equation of a line in slope-intercept form (y = mx + b), where y represents the gallons of water consumed and x represents the temperature.
First, let's determine the slope (m) using the given data points. The change in water consumption (y) divided by the change in temperature (x) will give us the slope.
Slope (m) = (change in y) / (change in x)
= (220 - 178) / (90 - 76)
= 42 / 14
= 3
Now that we have the slope, we can use one of the data points to determine the y-intercept (b). Let's use the first data point provided (90 degrees, 220 gallons of water consumed).
y = mx + b
220 = 3 * 90 + b
220 = 270 + b
b = -50
Therefore, the linear function to model the relationship between the gallons of water consumed and the temperature is:
y = 3x - 50
Part B: In the context of the problem, the slope (3) represents the rate of change in the gallons of water consumed for every one-degree increase in temperature. It tells us how much the amount of water consumed is expected to change when the temperature increases by one unit.
In this case, for every one-degree increase in temperature, the players consume an additional 3 gallons of water. So, the slope indicates that as the temperature rises, there is a proportional increase in the amount of water consumed by the players.