Linear relations > Linear models
1234Linear models

## Theory

Take a look at this applet.

Sometimes a relationship between two variables $y$ and $x$ is given in the form of a table of observations (measurements). If these points seem to lie (roughly) on a straight line, then you can set up a corresponding linear model. This comes with a linear function of the form $y=ax+b$.

If the line passes through $\left(10,210\right)$ and $\left(30,300\right)$, then you can determine the linear formula as follows:

• $x$ increases with $30-10=20$;

• $y$ increases with $300-210=90$;

• if therefore $x$ increases with $1$, then $y$ increases with $\frac{90}{20}=4.5$;

• the gradient of the line is therefore $4.5$;

• the required formula is then $y=4.5x+b$;

• $\left(10,210\right)$ has to lie on the line, therefore $210=4.5\cdot 10+b$, so $b=165$.

The formula of the line is: $y=4.5x+165$.