Linear Equations

In algebra now I'm solving some equations with 2 variables.

For example:

x + y = 10

Here are some of the solutions to this equation:

(1,9)
(-3,13)
(9,1)
(1.5,8.5)
(13,-3)
(1000,-990)
(0,10)
(-33.2,43.2)
.
.
.

As you can see there are infinite solutions (x,y) to this equation. In fact, there are infinite solutions to any equation with an x and y.

The best way to describe these solutions is with a graph.

This graph is always a straight line that extends in both directions to infinity.

The easiest way to draw these lines is by computing the x and y intercepts.

All you have to do is set x equal to 0 and solve for y. Then set y equal to 0 and solve for x.

Then you have two points that you can connect to draw the infinite line!

For example, the intercepts of x + y = 10 are (0,10) and (10,0).

The other common way to graph a line is with slope-intercept form: y = mx + b where m is the slope of the line and b is the y-intercept.