Algebra - Linear Equation

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Plotting of graph for the equation

y = ax + b

This simulation uses Java.

(1) Change the values of a, b. See how the graphs change.

 y  = x +

(After clicking on a drop down box, use the keyboard arrow keys to quickly change the values.)

(2) The yellow graph can be visualized as being created by adding the red and blue graphs together.

y1 = .x

,  

y2 = .

 y  = y1 + y2

(3) Zoom:

Background

Plotting the graph above might seem simple and obvious, but it was centuries before someone figured out how to do it.

It combines algebra (equations involving unknowns such as x and y) with geometry (shapes - lines, circles etc). Strange as it may seem now, these were two entirely separate fields of math. It was only in the 17th century that the French mathematician Descartes created Cartesian coordinates, which is what we use to plot graphs of equations.

Drawing a graph of an algebraic equation allows us to visualize the equation, helping us to understand it better.

Creating algebraic equations to describe geometric shapes, allows us to more easily analyze the shapes, using the power of algebra.