Graphing Linear Equations

Most of you know what a linear equation is.  You've not heard it called this, but you know what it is.  All the sequences we've had so far form linear equations.  So what are some things you can take away from what we've done with sequences?

1.  All linear equations have a constant rate of change.  As in, when x goes up by 1, y goes up by the same number each time, whether it's up by 2, 3, 5, etc.

We call this rate of change m.  In equation form, it's the number that is multiplied by x (remember inverses mean that it could be the number you're dividing by, too!).

These equations also have a constant number where x crosses the y-axis, called the y-intercept.  You find this by setting x to zero.  Then when you multiply by the change, the change falls out, leaving the intercept.  This intercept is called b.

A linear equation has a few different forms, but the most workable form is called the slope-intercept form.  This means we are solving for y by doing stuff to x.  So y = m * x + b

We can then graph the line on a coordinate plane based on using a process table for y = m * x + b.

You can see that demonstrated here: