

Subject:
writing equations
Category: Science > Math Asked by: twodsga List Price: $20.00 
Posted:
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. 

Subject:
Re: writing equations
Answered By: palitoyga on 15 Jun 2006 00:26 PDT Rated: 
Hello twodsga, Thankyou 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 yaxis. 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 yaxis 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 xaxis. 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 5579 = 24 The difference between the two x points is 6.001.50 = 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 doublecheck 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. 
twodsga
rated this answer:
greatthanks! I appreciate the linksit helped me understand the "gradiant"I keep confusing it with just the numerical difference between points on the graphi.e, 1.5 for x and 8 for y. 

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