document.write( "Question 471138: 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) \n" ); document.write( "
Algebra.Com's Answer #323150 by Theo(13342)\"\" \"About 
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slope intercept form of the equation of a straight line is:
\n" ); document.write( "y = mx + b
\n" ); document.write( "m is the slope
\n" ); document.write( "b is the y intercept
\n" ); document.write( "the slope is equal to (y2-y1) / (x2-x1)
\n" ); document.write( "x is the price per tile
\n" ); document.write( "y is the demand
\n" ); document.write( "x1 = 20
\n" ); document.write( "y1 = 42
\n" ); document.write( "x2 = 10
\n" ); document.write( "y2 = 52
\n" ); document.write( "m = (y2-y1) / (x2-x1) = 10 / -10 = -1
\n" ); document.write( "slope intercept form of the equation becomes:
\n" ); document.write( "y = -x + b because m = -1
\n" ); document.write( "point slope form of the equation for a straight line is:
\n" ); document.write( "y-y1 = m * (x-x1)
\n" ); document.write( "take any of the points and substitute for x1 and y1 to get:
\n" ); document.write( "we'll use (x1,y1) = (20,42)
\n" ); document.write( "we get:
\n" ); document.write( "y - 42 = -1 * (x-20)
\n" ); document.write( "this becomes:
\n" ); document.write( "y - 42 = -x + 20
\n" ); document.write( "add 42 to both sides of the equation to get:
\n" ); document.write( "y = -x + 62
\n" ); document.write( "our slope is -1 and our y intercept is 62
\n" ); document.write( "our equation is:
\n" ); document.write( "y = -x + 62
\n" ); document.write( "a graph of this equation is shown below:
\n" ); document.write( "\"graph%28600%2C600%2C-10%2C100%2C-10%2C70%2C-x%2B62%2C42%2C52%29\"
\n" ); document.write( "I drew 2 horizontal lines at y = 52 and y = 42 so you can better see that, when y = 52, x = 10, and when y = 42, x = 20.
\n" ); document.write( "x is the price per tile.
\n" ); document.write( "y is the demand in number of tiles.
\n" ); document.write( "just drop a vertical line from the intersection of those 2 horizontal lines with the line of the equation to see the value of x.
\n" ); document.write( "it will be in the area of x = 10, and x = 20.
\n" ); document.write( "plugging x = 10 and x = 20 in the equation gets you the exact value of y.
\n" ); document.write( "alternatively, plugging y = 52 and y = 42 in the equation gets you the exact value of x.
\n" ); document.write( "for example:
\n" ); document.write( "the equation is y = -x + 62
\n" ); document.write( "when y = 52, this equation becomes 52 = -x + 62
\n" ); document.write( "add x to both sides of the equation and subtract 52 from both sides of this equation gets you x = 10.
\n" ); document.write( "this graph is showing the demand per month (y) based on the price per tile (x).
\n" ); document.write( " \n" ); document.write( "
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