Question

HELP PLEASE 40 POINTS 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. 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. AND IT IS NOT QUESTION AND ANSWER PLEASE LOOK AT THE GRAPH AND READ THE PARAGRAPH

Answer 1

see below

Explanation:

Part A

Since the lines goes through the point (0,0) the graph is proportional. We can find the rate of change by take the price of corn and dividing by the number of bushels

24/3 = 8 dollars/ bushel

Part B

Previous Year Number of Bushels Price of Corn (dollars)

3 21

6 42

9 63

12 84

We can find the rate of change for the previous year by using the slope formula

m = (y2-y1)/(x2-x1)

m = (84-63)/(12-9)

=21 / 3

= 7

The previous year was 7 dollars per bushel

The increase was 8-7 = 1 dollar per bushel

Answer 2

Part A: 8 dollars/brushel

Part B: 1 dollar/brushel

Explanation:

Without reading the question you can already conclude that this is a linear equation. Also, we can easily get the linear function:

`f(x)=8x`

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.

We know that a linear function has a constant rate of change, and that is called SLOPE.

In order to calculate the slope of the linear function:

`$m=(\Delta y)/(\Delta x) = (y_(2)- y_(1))/(x_(2)-x_(1))= (48-24)/(6-3)= (24)/(3) = 8$`

Therefore, the rate of change of a bushel of corn in the current year is 8

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.

Previous Year Number of Bushels Price of Corn (dollars)

Ordered pairs:

`(3, 21); (6, 42); (9, 63); (12, 84)`

Let's calculate the slope again.

`$m=(\Delta y)/(\Delta x) = (y_(2)- y_(1))/(x_(2)-x_(1))= (42-21)/(6-3)= (21)/(3) = 7$`

The difference is 1 dollar/brushel.