Height and WeightDate: 10/30/96 at 23:58:40 From: Joey Fang Subject: Height and Weight Dr. Math, I am an 8th grader in Algebra I Honors. My school has these problems called "POWs". They are really hard and require much thinking. I am stuck on one. The problem asks to find a formula for predicting a person's weight when all you know is his/her height. Could you please help me out? Thanks for your time, Joey Fang Date: 10/31/96 at 13:48:12 From: Doctor Jerry Subject: Re: Height and Weight Dear Joey Fang, I don't know if you've studied graphs of equations yet. For example, the graph of the equation y = 2x + 3 is a line in the (x,y)-plane. Even if you don't know much about graphs, perhaps we can use the equation y = 2x + 3 to discuss your problem. If y is weight (in pounds) and x is height (in feet), then if we were to use the equation y = 2x + 3 to predict weight, we would say, for example, that if the person's height were x = 5 feet, then their weight would be y = 2*x + 3 = 2*5 + 3 = 8 pounds. Of course, the numbers 2 and 3 in the equation y = 2x + 3 are not very good for actual heights and weights. If you want to find numbers m and b so that the equation y = m*x + b predicts weight y when you know height x, I think you should talk to some kids in your class and ask them for their heights and weights. Plot these on a graph and then try to guess the line that most nearly goes through the points that you've plotted. It's not hard to figure out the m and b for the line that you decide on. Note that when x = 0, y = b. So, just draw the line so that it crosses the y-axis. This will give you b. Substitute this into the equation y = m*x + b for the next step. Look closely at the line you drew and try to locate a point with known coordinates that lies on the line. I'll give an example. Suppose you found that b = 50, so the line would be y = m*x + 50. Suppose that when you look at your graph you find that the line goes through or almost goes through the point (4, 80). Then just substitute into the equation: 80 = m*4+50. Solve this equation for m = 15/2. Your equation will be y = (15/2)*x+50. Have you understood all of this? If not, please write again. -Doctor Jerry, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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