# Linear Functions - The Basics

## 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.