Height and Weight

Date: 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/