Meg plotted the graph below to show the relationship between the temperature of her city and the number of people at a swimming pool:
Main title on the graph is Swimming Pool Population. Graph shows 0 to 30 on x axis at increments of 5 and 0 to 12 on y axis at increments of 1. The label on the x axis is Temperature in degree C, and the label on the y axis is Number of People at the Pool. Dots are made at the ordered pairs 2.5, 1 and 5, 2 and 7.5, 2 and 7.5, 3 and 7.5, 4 and 10, 5 and 10, 6 and 12.5, 6 and 15, 7 and 15, 8 and 17.5, 5 and 17.5, 7 and 20, 9 and 22.5, 7 and 22.5, 9 and 25, 11 and 27.5, 12.
Part A: In your own words, describe the relationship between the temperature of the city and the number of people at the swimming pool. (5 points)
Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate slope and y-intercept. (5 points)
Part A: The graph shows that as the temperature of the city increases, the number of people at the swimming pool also tends to increase. However, there are some fluctuations in the number of people at certain temperatures, indicating that there may be other factors influencing the population at the pool.
Part B: To make the line of best fit, we can look for an approximate trend in the data points. By eyeballing the points, we can see that they generally follow a linear pattern.
To calculate the slope, we can choose two points that are easy to work with. Let's use the points (5, 10) and (12, 27.5):
Slope = (27.5 - 10) / (12 - 5) = 17.5 / 7 = 2.5
To calculate the y-intercept, we can pick a point and use the slope we just calculated. Let's use the point (5, 10):
y = mx + c
10 = 2.5(5) + c
10 = 12.5 + c
c = -2.5
Therefore, the equation for the line of best fit is:
y = 2.5x - 2.5