SOLUTION: A home-made lefsa enterprise estimates that they can sell 30 dozen lefsa at $3.00 per dozen and 25 dozen lefsa at $4.00 per dozen. write a linear equation for the amount of lefsa s

Question 180188: A home-made lefsa enterprise estimates that they can sell 30 dozen lefsa at $3.00 per dozen and 25 dozen lefsa at $4.00 per dozen. write a linear equation for the amount of lefsa sold in terms of the price per dozen. use your equation to approximate the amount of lefsa sold at $5.00 per dozen.
thanks for helping me on this!!
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A home-made lefsa enterprise estimates that they can sell 30 dozen lefsa at $3.00 per dozen and 25 dozen lefsa at $4.00 per dozen. write a linear equation for the amount of lefsa sold in terms of the price per dozen. use your equation to approximate the amount of lefsa sold at $5.00 per dozen.
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You have two points of the form (price,lefsa)
They have (3,30) and (4,25)
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m = (25-30)/(4-3) = -5
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You have m=-5 and y = 25 when x = 4; solve for b in the form y = mx + b
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25 = -5*4 + b
b = 45
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lefsa(in dozens) = -5(price) + 45
lefsa($5) = -5*5 + 45
lefsa($5) = 20 dozen
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Cheers,
Stan H.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Here you have a situation where the value 3 maps to the value 30 and the value 4 maps to the value 25. This is exactly the same as saying that you have two ordered pairs defining a straight line and the two ordered pairs are (3, 30) and (4, 25).

Notice that when the x value increases by 1, the y value decreases by 5. That means that the slope of our line is -5. Also notice, using this slope number, that 2 would map to 35, 1 would map to 40, and 0 would map to 45. That tells us that the y-intercept of the line is 45.

Now we can write the equation in slope intercept form directly:

To calculate the sales at a $5 price point, substitute 5 for x and do the arithmetic.

John

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