Question 201175
a) Using Algebra one can easily transform the two equations into the familiar slope-intercept form: y = mx + b
S = 200x + 5000
D = -100x + 9500
Therefore the graph of each will be a line. For S, the y-intercept will be 5000 and the slope will be 200. For D, the y-intercept will be 9500 and the slope will be -100.
b) Either from the graph or from the slope, you can tell that as the price goes up (in other words as you go from left to right on the graph) S, the supply, goes up, too.
c) Similarly D, the demand, goes down as the price goes up.
d) Since S = D at the equilibrium price, 200x + 5000 = -100x + 9500. To find the equilibrium price solve this equation:
200x + 5000 = -100x + 9500
Add 100x to both sides:
200x + 5000 + 100x = -100x + 9500 + 100x
300x + 5000 = 9500
Subtract 5000 from both sides:
300x + 5000 - 5000 = 9500 - 5000
300x = 4500
Divide both sides by 300
(300x)/300 = (4500)/300
x = 15
Therefore the equilibrium price is $15.00