Meg plotted the graph below to show the relationship between the temperature of her city and the number of sweaters sold at a store:
Main title on the graph is Sweater Sale. 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 Sweaters Sold. Dots are made at the ordered pairs 0, 12 and 2.5, 10 and 2.5, 11 and 5, 10 and 7.5, 9 and 7.5, 10 and 10, 7 and 12.5, 6 and 12.5, 8 and 15, 4 and 15, 7 and 17.5, 5 and 20, 1 and 20, 3 and 22.5, 9 and 25, 1 and 27.5, 1.
Part A: In your own words, describe the relationship between the temperature of the city and the sale of sweaters in the city. (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 there is a negative relationship between the temperature of the city and the number of sweaters sold at the store. As the temperature increases, the number of sweaters sold decreases.
Part B: To make the line of best fit, we can draw a line that visually represents the general trend of the data points. To calculate the slope and y-intercept, we can choose two points that are easy to read on the graph. Let's use the points (0, 12) and (5, 10):
Slope = (10-12)/(5-0) = -2/5 = -0.4
Using the point (0, 12) and the calculated slope of -0.4:
y = mx + b
12 = -0.4*0 + b
b = 12
Therefore, the equation of the line of best fit is y = -0.4x + 12.