Question 1111563: You need to find a formula for the number of cars produced by a new plant that was opened 20 days ago. You are told that four days ago the plant had 370 cars on hand, and that yesterday it had 400 cars on hand. You also are told that some of these cars came from previous inventory. Assume that the plant produces cars at this same rate and has produced them at this same rate since it opened.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you are told that 4 days ago, the plant has 370 cars on hand.
you are also told that yesterday, which is 1 day ago, the plant had 400 cars on hand.
let x equal the number of days since the plant opened.
since it opened 20 days ago, then x = 20 today.
4 days ago, x must have been equal to 16.
1 day ago, x must have been equal to 19.
between x = 16 and x = 19, there was an increase in inventory of 400 - 370 = 30 cars.
that would be an increase of 30 / 3 = 10 cars a day.
that would be the slope of your equation in slope intercept form of y = mx + b
m is the slope
b is the y-intercept.
the equation becomes y = 10x + b
to solve for b, you would replace x and y with known points that satisfy the equation.
those points would be y = 370 when x = 16, and y = 400 when x = 19.
we'll use y = 370 when x = 16.
that would be the coordinate point of (16,370)
when x = 16 and y = 370, your equation of y = 10x + b becomes 370 = 10 * 16 + b.
solve for b in this equation to get:
b = 370 - 10 * 16 which becomes b = 370 - 160 which becomes b = 210.
your equation now becomes y = 10x + 210.
this equation says that the plant opened with 210 cars in inventory and made 10 additional cars per day since then.
the graph of this equation looks like this:
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