Question 1162780: A manufacturing company finds that they can sell 450 items at $2.00 per item and 225 items at $3.50 per item. If the relationship between the number of items sold x and the price per item p is a linear one:
Find a formula that gives x in terms of p: x=
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you want a linear relationship between x and p
that would be a straight line equation with the general form of y = mx + b
m is the slope
b is the y-intercept
since you x in terms of p, then:
let y = x
let x = p
the equation of y = mx + b is the same as the equation of x = mp + b after you replace y with x and x with p.
in the equation of x = mp + b, you have coordinate points in the form of (p,x)
since y = x and x = p, this is the same as the form of (x,y), which is the standard form of the linear equation coordinate points.
we'll work with x = mp + b and then later translate to y = mx + b for graphing purposes.
your standard form is x = mp + b with coordinate points of (p,x).
you have two coordinate points.
they are (2,450) and (3.5,225)
m is equal to slope which is equal to (y2-y1)/(x2-x1) which is then translated to (x2-x1)/p2-p1 when you replace y with x and x with p.
assign (2,450) to (p1,x1) and assign (3.5,225) to (p2,x2) and the slope equation becomes (225-450)/(3.5-2) which becomes -225/1.5 = -150.
your slope is -150 and your equation of x = mp + b becomes x = -150 * p + b
replace x and p with one of the points to solve for b.
i used (2,450).
the equation of x = mp + b becomes 450 = -150 * 2 + b
solve for b to get b = 750.
the equation becomes x = -150 * p + 750.
that's your final equation.
to graph it, i replaced x ith y and p with x to get y = -150 * x + 750.
the graph is shown below.
the equation of y = -150 * x + 750 is for graphing purposes only.
your solution is the equation of x = -150 * p + 750
x represents the number of items sold.
p represents the price of each item.
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