SOLUTION: Just wanting to see if I am doing this right? In this problem, we analyze the profit found for sales of decorative tiles. A demand equation (sometimes called a demand curve) show

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Just wanting to see if I am doing this right? In this problem, we analyze the profit found for sales of decorative tiles. A demand equation (sometimes called a demand curve) show      Log On


   

Question 614207: Just wanting to see if I am doing this right?
In this problem, we analyze the profit found for sales of decorative tiles. A demand equation (sometimes called a demand curve) shows how much money people would pay for a product depending on how much of that product is available on the open market. Often, the demand equation is found empirically (through experiment, or market research).
Suppose a market research company finds that at a price of p = $20, they would sell x = 42 tiles each month. If they lower the price to p = $10, then more people would purchase the tile, and they can expect to sell x = 52 tiles in a month’s time. Find the equation of the line for the demand equation. Write your answer in the form p = mx + b. Hint: Write an equation using two points in the form (x,p).
p= -x+62

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
the two points are (42,20) and (52,10)
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (42,20) and (52,10)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: (x%5B1%5D,y%5B1%5D) is the first point (42,20) and (x%5B2%5D,y%5B2%5D) is the second point (52,10))


m=%2810-20%29%2F%2852-42%29 Plug in y%5B2%5D=10,y%5B1%5D=20,x%5B2%5D=52,x%5B1%5D=42 (these are the coordinates of given points)


m=+-10%2F10 Subtract the terms in the numerator 10-20 to get -10. Subtract the terms in the denominator 52-42 to get 10




m=-1 Reduce



So the slope is

m=-1





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Now let's use the point-slope formula to find the equation of the line:




------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and (x%5B1%5D,y%5B1%5D) is one of the given points


So lets use the Point-Slope Formula to find the equation of the line


y-20=%28-1%29%28x-42%29 Plug in m=-1, x%5B1%5D=42, and y%5B1%5D=20 (these values are given)



y-20=-x%2B%28-1%29%28-42%29 Distribute -1


y-20=-x%2B42 Multiply -1 and -42 to get 42%2F1. Now reduce 42%2F1 to get 42

y=-x%2B42%2B20 Add 20 to both sides to isolate y


y=-x%2B62 Combine like terms 42 and 20 to get 62

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Answer:



So the equation of the line which goes through the points (42,20) and (52,10) is:y=-x%2B62


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-1 and the y-intercept is b=62


Notice if we graph the equation y=-x%2B62 and plot the points (42,20) and (52,10), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=-x%2B62 through the points (42,20) and (52,10)


Notice how the two points lie on the line. This graphically verifies our answer.