SOLUTION: The owners of a movies theater know that the number of people who attend is a function of the price of the ticket. The teacher has a capacity of 240 people. If tickets are sold for

Question 1152409: The owners of a movies theater know that the number of people who attend is a function of the price of the ticket. The teacher has a capacity of 240 people. If tickets are sold for $1 the theater will be fulled and if the theater charges 21 it will be empty
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
when the price of the ticket is 1 dollar, then 240 tickets are sold.
then the price of the ticket is 21 dollars, then 0 tickets are sold.
the slope intercept form of the equation of a straight line is"
y = mx + b
m is he slope.
b is the y-intercept
if you let x = the price of the ticket and y represent the number of tickets sold, then you have two point from which to create you equation.
they will be (x,y) = (1,240) and (21,0)
what these points tell you is that when x = 1, y = 240, and when x = 21, y = 0.
if you call these points (x1,y1) = (1,240) and (x2,y2) = 21,0), than you can fit these points into the slope equation, which is:
slope = (y2 - y1) / (x2 - x1)
that becomes (0 - 240) / (21 - 1) = -240 / 20 = -12
your slope is -12.
the equation of y = mx + b becomes:
y = -12 * x + b
to solve for b, replace x and y with the values of either one of the points.
i used (1,240)
the equation becomes 240 = -12 * 1 + b
simplify to get 240 = -12 + b
solve for b to get b = 252
the equation becomes y = -12 * x + 252

the equation can be graphed as shown below:

$$$

in the graph, x represents the price of the ticket and y represents the number of tickets sold.

when x = 1, y = 240
when x = 21, y = 0
when the price of the ticket is 1 dollar, 240 tickets are sold.
when the price of the ticket is 21 dollars, 0 tickets are sold.

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