At a price of $ 1.94 per bushel, the supply corn in 9,800 million bushel and the demand is 9, 300 million bushel. At a price of $1.82 per bushel, the supply is 9,400 million bushels and the demand is 9, 500 million bushels.

A, find a price-supply equation of the form p=mx + b
B, Find a price-demand equation of the form p=mx + b
C, Find the equilibrium point.
D, graph the price-supply equation, price-demand equation, and equilibrium point in the same coordinate system.

A. To find the price-supply equation, we need to find the equation in the form p = mx + b. Here, p represents the price and x represents the quantity supplied.

Using the given data points:
(1.94, 9800) and (1.82, 9400)

We can find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)

m = (9400 - 9800) / (1.82 - 1.94)
m = -1000 / (-0.12)
m = 8333.33...

Next, we can find b (the y-intercept) by substituting the coordinates of one of the points into the equation:
p = mx + b
1.94 = 8333.33... * 1.94 + b
1.94 = 16111.11... + b
b = 1.94 - 16111.11...
b = -16109.17...

Therefore, the price-supply equation is:
p = 8333.33...x - 16109.17...

B. To find the price-demand equation, we need to follow a similar process. Here, p represents the price and x represents the quantity demanded.

Using the given data points:
(1.94, 9300) and (1.82, 9500)

We can calculate the slope (m) using the formula mentioned before:
m = (y2 - y1) / (x2 - x1)

m = (9500 - 9300) / (1.82 - 1.94)
m = 200 / (-0.12)
m = -1666.67...

Next, we substitute the coordinates of one of the points into the equation:
p = mx + b
1.94 = -1666.67... * 1.94 + b
1.94 = -3233.33... + b
b = 1.94 + 3233.33...
b = 3235.27...

Therefore, the price-demand equation is:
p = -1666.67...x + 3235.27...

C. The equilibrium point represents the price and quantity at which supply and demand are equal. To find it, we set the quantity supplied (x) equal to the quantity demanded (x) and solve for p (price).

From the price-supply equation:
p = 8333.33...x - 16109.17...

Setting this equation equal to the price-demand equation:
8333.33...x - 16109.17... = -1666.67...x + 3235.27...

Combine like terms:
9999.999...x = 19344.44...

Divide both sides by 9999.999...:
x = 1.9344...

Substitute this value of x into either equation to find the price (p):
p = 8333.33... * 1.9344... - 16109.17...
p ≈ 15992

Therefore, the equilibrium point is approximately (1.9344..., 15992).

D. To graph the price-supply equation, the price-demand equation, and the equilibrium point in the same coordinate system, create a graph with the price (p) on the y-axis and the quantity (x) on the x-axis.

Plot the price-supply equation (p = 8333.33...x - 16109.17...) and the price-demand equation (p = -1666.67...x + 3235.27...) as lines. The equilibrium point (1.9344..., 15992) represents the intersection of these lines.

Note: Since the equations are linear, you only need to plot two points per line to draw the lines accurately.