Question 251674
let x1 = 120 cents
let x2 = 140 cents


for the supply equation:


let y1 = 350
let y2 = 850


for the demand equation:


let y1 = 980
let y2 = 850


the x-axis will represent the price per bushel in cents.


the y-axis will represent the number of bushels.


example:


when x = 120, y = 980 for the demand equation, and y = 350 for the supply equation.


supply equation:


since this is a linear equation, it will take the slope-intercept form of:


y = mx + b where m is the slope and b is the y-intercept.


slope is equal to (y2-y1)/(x2-x1) = (850-350)/(140-120) = 500/20 = 25


substitute any of the 2 points to find the y-intercept.


equation is y = 25x + b


substitute (140,850) to get 850 = 25*140 + b


solve for b to get b = 850 - (25*140) = -2650


your supply equation is:


y = 25x - 2650


demand equation:


since this is a linear equation, it will take the slope-intercept form of:


y = mx + b where m is the slope and b is the y-intercept.


slope is equal to (y2-y1)/(x2-x1) = (850-980)/(140-120) = -130/20 = -6.5


substitute any of the 2 points to find the y-intercept.


equation is y = -6.5x + b


substitute (140,850) to get 850 = -6.5*140 + b


solve for b to get b = 850 - (-6.5*140) = 1760


your demand equation is:


y = -6.5x + 1760


you have two linear equations.


they are:


y = 25x - 2650 (supply equation)


y = -6.5x + 1760 (demand equation)


graph these equations to get:


{{{graph(600,600,-100,500,-5000,5000,25x-2650,-6.5x+1760)}}}


your demand equation is sloping downwards.


as the price increases, the demand goes down.


your supply equation is sloping upwards.


as the price increases, the supply goes up.


your equilibrium point is when x = 140 cents which is equivalent to $1.40 per bushel.


the equilibrium point is when the demand equals the supply.


that is the point where the graph of the supply and demand equations intersects.