# Linear function

Linear functions are functions of the form:

the domain of which belongs to the set of real numbers .

and the codomain also belongs to the set of real numbers .

This formula is the is also call the straight line function, because its graph is a straight line.

## The slope m

The constant m of a linear function is the slope or gradient of the function. It tells us how steep the line is, and if it is decaying or growing.

m < 0: The function is decaying

m > 0: The function is growing

m = 0: The function is constant

## The constant b

The constant b indicates where the straight line intersects the y-axis. This will be in the point (0,b).

If b is 0, the function is said to be direct proportional, and its graph passes through the origin (0,0).

## Calculation of m and b with two points given

If a straight line is passing through two points with the coordinates (x_{1}, y_{1}) and (x_{2}, y_{2}), the slope m can be calculated like this:

when m is known you can calculate b:

## Linear growth

If x increases by 1, the change of y will be m.

If x increases by , the change of y will be .

This relationship is given by the formula:

## Simple linear regression

If you have two sets of data, and you want to know, if there is a linear relationship between them, you can plot the data in a coordinate system and see if they fit into a straight line, or you can use a calculator to make the linear regression.

## Finding the slope with an angle

If you know the angle θ between the x-axis and a line, you can calculate m of the linear function by using tangent: