The graph shows the prices of different numbers of bushels of corn at a store in the current year. The table shows the prices of different numbers of bushels of corn at the same store in the previous year.
A graph shows Number of Bushels on x-axis and Price of Corn in dollars on y-axis. The x-axis scale is shown from 0 to 14 at increments of 2, and the y-axis scale is shown from 0 to 98 at increments of 14. A straight line joins the ordered pairs 2, 14 and 4, 28 and 6, 42 and 8, 56 and 10, 70 and 12, 84.
Previous Year
Number of Bushels
Price of Corn (dollars)
2
10
4
20
6
30
8
40
Part A: Describe in words how you can find the rate of change of a bushel of corn in the current year, and find the value. (5 points)
Part B: How many dollars more is the price of a bushel of corn in the current year than the price of a bushel of corn in the previous year? Show your work. (5 points)
Part A: To find the rate of change of a bushel of corn in the current year, we need to calculate the slope of the line on the graph. We can do this by finding the difference in the prices of corn for two different quantities of bushels and dividing it by the difference in the quantities of bushels.
Using the points (2, 14) and (4, 28):
Slope = (28-14)/(4-2)
Slope = 14/2
Slope = 7
Therefore, the rate of change of a bushel of corn in the current year is $7 per bushel.
Part B: To find how many dollars more the price of a bushel of corn in the current year is compared to the price in the previous year, we need to calculate the difference in prices for the same quantity of bushels.
From the table, we see that the price of a bushel of corn in the previous year was $10.
From the graph, the price of a bushel of corn in the current year is $14.
Price difference = $14 - $10
Price difference = $4
Therefore, the price of a bushel of corn in the current year is $4 more than the price in the previous year.