Question 1111563
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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