# Equation for set of linear graph lines

## Homework Statement

Have graph of dependent variable x and independent variable y. The graph contains 6 linear lines representing 6 discrete constants z.
I'm looking for one equation that would represent all 6 of the linear lines...

## The Attempt at a Solution

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Without seeing the y=y(x) equations for the 6 lines, it would be difficult for me to give you a helpful answer to the general problem. Can you provide a little more details? Are the lines parallel?

The lines are not paralell. I will attempt to attach a picture/copy of the multi-line graph...
Each of the lines represent discrete and constant (tire size in this case). I'd like the generalized equation to address the tire size as a variable.

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Yeah, it would be easier if you could post a picture or just something a little more, because I'll have to explain by example... and making up an example seems more trouble than its worth.

Yeah, it would be easier if you could post a picture or just something a little more, because I'll have to explain by example... and making up an example seems more trouble than its worth.

Hopefully I have the multi-linear line graph attached for your review and comment on a generalized equation for all parameters.
Fred

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Okay, so hopefully I am reading the graph right. My thoughts on this would be to read off the slopes of each line of the graph and correlate them to the tire width given for each line.

By quickly reading the graph I come up with these numbers and then looked for a relationship between them.
Tire Width(mm) vs Pressure-Load Slope (psi/kg):

$$37mm \longrightarrow {50psi \over 50kg}$$

$$32mm \longrightarrow {50psi \over 40kg}$$

$$28mm \longrightarrow {90psi \over 55kg}$$

$$25mm \longrightarrow {130psi \over 65kg}$$

$$20mm \longrightarrow {110psi \over 40kg}$$

There are many relationships we could draw from these numbers, since the slopes aren't exact, it doesn't matter too much what you pick. I had Calc do a couple of different ones for me.

http://img522.imageshack.us/img522/4997/testzan.jpg [Broken]
http://img4.imageshack.us/img4/8683/testtfv.jpg [Broken]

The slopes are defined in terms of your original (x,y) coordinates, and the z (or x on my axis) is the width variable.

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