Jack plotted the graph below to show the relationship between the temperature of his city and the number of ice cream cones he sold daily:
Main title on graph is Ice Cream Cone Sale. Graph shows 0 to 30 on x axis at increments of 5 and 0 to 60 on y axis at increments of 10. The label on the x axis is Temperature in degree C, and the label on the y axis is Number of Ice Cream Cones Sold. Dots are made at the ordered pairs 0, 5 and 5, 15 and 7.5, 15 and 10, 24 and 10, 28 and 12, 32 and 12.5, 25 and 12.5, 30 and 15, 35 and 15, 40 and 17.5, 35 and 20, 45 and 22.5, 36 and 23, 46 and 25, 55 and 27.5, 60.
Part A: In your own words, describe the relationship between the temperature of the city and the number of ice cream cones sold. (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
Part A: The graph shows a positive correlation between the temperature of Jack's city and the number of ice cream cones he sells daily. As the temperature increases, the number of ice cream cones sold also increases.
Part B: To make the line of best fit, we can draw a straight line that passes through the middle of the points on the graph. We can calculate the slope by selecting two points (e.g. (0, 5) and (60, 60)) and using the formula for slope: (y2 - y1) / (x2 - x1). The y-intercept can be estimated by looking at where the line intersects the y-axis.
Calculating the slope:
Slope = (60 - 5) / (60 - 0) = 55 / 60 = 11/12
Estimating the y-intercept:
By looking at the graph, the y-intercept is approximately around 5.
Therefore, the line of best fit has an approximate slope of 11/12 and a y-intercept of around 5.