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 21 at increments of 3, and the y-axis scale is shown from 0 to 168 at increments of 24. A straight line joins the ordered pairs 3, 24 and 6, 48 and 9, 72 and 12, 96 and 15, 120 and 18, 144.
Previous Year
Number of Bushels
Price of Corn (dollars)
3
21
6
42
9
63
12
84
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, you can determine the slope of the line on the graph. The slope represents the change in price for each additional bushel of corn. To find the slope, you can choose two points on the line and use the formula:
Slope = (Change in y) / (Change in x)
For example, you can choose the points (3, 24) and (6, 48) on the line. The change in y is 48 - 24 = 24, and the change in x is 6 - 3 = 3. Therefore, the slope is 24 / 3 = 8 dollars per bushel.
Part B: To find how many dollars more the price of a bushel of corn is in the current year compared to the previous year, you can subtract the price of a bushel of corn in the previous year from the price of a bushel of corn in the current year. Using the information from the table, the price of a bushel of corn in the previous year is 84 dollars. Let's assume the price of a bushel of corn in the current year is 150 dollars.
The difference in price is 150 - 84 = 66 dollars.
Therefore, the price of a bushel of corn in the current year is 66 dollars more than the price of a bushel of corn in the previous year.