Expert: David Montiel - 11/12/2009

Question
I am having a hard time understanding how to get the linear function y=mx+b out of this table.

The Exponential model is easy to understand for me though.
Any help on Linear functions would be appreciated, the part I'm having trouble with is, that the x values are somewhat oddly spaced out.

x 1  3  4  7  9  12  15
________________________

y 3  7  8  15 18 24  31

Thanks!

Answer
Hello Christopher,

Find the slope for each pair of data. For instance the first pair will be

x1=1,  y1=3
x2=3,  y2=7

so the slope for the first pair of points (x1,y1) and (x2,y2) is

slope = (y2-y1)/(x2-x1) = (7-3)/(3-1) = 4/2 = 2

Repeat that for each remaining pair of points (x2,y2), (x3,y3), etc.

If you get the same value for the slope (slope = 2) for each case means that your data describe a linear function, they fit a staight line...

If it turns out that for two or more pairs, the slope isn't the same, you can also do a linear fit, but not an exact one.

Let's say that indeed slope =2 for all pairs, then for your equation y=mx+b. the value of "m" is

m=slope

and the value of b can be calculated by substituting a single point say (x1,y1) into the linear equation.

y-y1 = m(x-x1)

You can always write this in the form y=mx+b to get "b". Try it.

Hope this is clear,
David