# Linear Functions - The Basics

- Author:
- Simona Riva

- Topic:
- Functions, Function Graph, Linear Functions

## Graph of a linear function and slope

The graph of a function of the form is a

*line*. This is why all the functions of this type are named*linear functions*. If we know the coordinates of two points of the function, and , we can calculate the*slope*of the line: . This is a constant value: however you choose two points on the line, the value of*m*is always the same.## Try it yourself...

In the app below, move points and , then enter in the input box the value of the slope of the line that you have defined.
Select

*Check answer*to get a feedback for your answer and view the solution of this exercise. Deselect*Check answer*to create a new line and calculate its slope.## When things go wrong algebraically...

If you have the equation of a linear function and the coordinates of two of its points, and , you can calculate:
- the value of the

*y*-intercept - the value of the slope, using the formula . Move points*A*and*B*in the app above, and align them vertically. You will discover which is the algebraic issue that is generated by such a configuration.## ... and geometrically

Move points *A* and *B* in the app above, and align them vertically.
Observe the graph of the line.
Is this the graph of a *linear function*?
Explain your conjectures.