At a price of 2.26 per bushel, the supply of a certain grain is 7500 million bushels and the demand is 7600 million bushels. At a price of 2.31 per bushel, the supply is 7900 million bushels and the demand is 7500 million bushels. (A) Find a price -Supply equation of the form p=mx+b where p is the price in dollars and x is the supply in millions of bushels. (B) Find a price -demand equation of the form p=mx+b where p is the price in dollars and x is the demand in millions of bushels. (C) Find the equilibrium point. (D) Graph the price supply equation, price-demand equation, and equilibrium point t in the same coordinate system (A) The price-supply equation is p=0.000125x+1.3225 (Type an exact answer.) (B) The price-demand equation is p = p=-0.0005x+6.06 (Type an exact answer.) (C) The equilibrium point is square (Type an ordered pair Type an exact answer.Use integers or decimals for any numbers in the expression.)

To find the price-supply equation, we can use the given data points (7500, 2.26) and (7900, 2.31). We can use these points to find the slope (m) and the y-intercept (b) of the equation in the form p = mx + b.<br /><br />Step 1: Find the slope (m) using the formula:<br />m = (y2 - y1) / (x2 - x1)<br />m = (2.31 - 2.26) / (7900 - 7500)<br />m = 0.000125<br /><br />Step 2: Substitute one of the points into the equation p = mx + b to solve for b.<br />Using the point (7500, 2.26):<br />2.26 = 0.000125(7500) + b<br />b = 1.3225<br /><br />Therefore, the price-supply equation is:<br />p = 0.000125x + 1.3225<br /><br />To find the price-demand equation, we can use the given data points (7600, 2.26) and (7500, 2.31). We can use these points to find the slope (m) and the y-intercept (b) of the equation in the form p = mx + b.<br /><br />Step 1: Find the slope (m) using the formula:<br />m = (y2 - y1) / (x2 - x1)<br />m = (2.26 - 2.31) / (7600 - 7500)<br />m = -0.0005<br /><br />Step 2: Substitute one of the points into the equation p = mx + b to solve for b.<br />Using the point (7600, 2.26):<br />2.26 = -0.0005(7600) + b<br />b = 6.06<br /><br />Therefore, the price-demand equation is:<br />p = -0.0005x + 6.06<br /><br />To find the equilibrium point, we need to set the price-supply equation equal to the price-demand equation and solve for x.<br /><br />0.000125x + 1.3225 = -0.0005x + 6.06<br />0.000625x = 4.7375<br />x = 7540<br /><br />Now, substitute x back into either the price-supply equation or the price-demand equation to find the equilibrium price (p).<br /><br />Using the price-supply equation:<br />p = 0.000125(7540) + 1.3225<br />p = 2.30<br /><br />Therefore, the equilibrium point is:<br />(7540, 2.30)<br /><br />So, the final answers are:<br />(A) The price-supply equation is p = 0.000125x + 1.3225<br />(B) The price-demand equation is p = -0.0005x + 6.06<br />(C) The equilibrium point is (7540, 2.30)