Category: Science > Math
Asked by: twods-ga
List Price: $20.00
14 Jun 2006 23:16 PDT
Expires: 14 Jul 2006 23:16 PDT
Question ID: 738299
write an equation for this story problem: As the price of a car wash increases by $1.50, 8 fewer people will visit the car wash. The "y" intercept is 87. So at $1.50, 79 people will go; at $3.00, 71 people; at $4.50, 63 people; at $6.00, 55 people, etc.
Re: writing equations
Answered By: palitoy-ga on 15 Jun 2006 00:26 PDT
Hello twods-ga, Thank-you for your question. The easiest way to solve this question is to tabulate the information and draw a quick graph. I find it is always easier to visualise the data when you can see a picture of what is going on! x y ========= 0.00 87 1.50 79 3.00 71 4.50 63 6.00 55 If you plot this it is obvious to see that the data produces a straight line on your graph. The equation of all straight lines is of the format y = mx + c where m is the gradient of the slope and c is the intercept of the slope on the y-axis. This can be verified here: http://www.mathsisfun.com/equation_of_line.html If we draw a line through the points on our graph we can see that the line crosses the y-axis at 87. This information is also given to us in the question and the proof of this concept can be seen here: http://www.mathsisfun.com/y_intercept.html To work out the gradient of the graph we need to know how many units the line drops in how many units along the x-axis. We can do this by taking 2 data point pairs and finding the difference between the paired values and then dividing the results. To see verification of this you can visit: http://www.mathsisfun.com/gradient.html Let's take these points: 1.50 & 79 6.00 & 55 The difference between the two y points is 55-79 = -24 The difference between the two x points is 6.00-1.50 = 4.50 Dividing these two results gives us the gradient of the line: -24 / 4.50 = -5.33333333 (or -5 and one third or -5 point 3 recurring). Putting all this information together... we now know the intercept (c) on the line is 87, the gradient (m) of the line is -5 1/3 and that an equation of a straight line is y = mx + c. The equation is therefore y = -5.333333333x + 87 This equation could also be written as: y = -(16/3)x + 87 You can double-check the solution by inserting some of the known values of x and y into the equation. If you require any further assistance on this subject please do not hesitate to ask for clarification.
rated this answer:
great--thanks! I appreciate the links--it helped me understand the "gradiant"--I keep confusing it with just the numerical difference between points on the graph--i.e, 1.5 for x and 8 for y.
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