Algebra ( Period 1)

Graphing Systems of Linear Equations 6-1

We just learned how to graph a single linear equation (a line).

We graphed in standard form using intercepts, in slope-intercept form by graphing the y-intercept and then counting the slope to another point, and in point-slope form by graphing a random point and then counting the slope to another point.

If two or more lines are graphed on the same coordinate plane, one of three things will happen:

1. They will intersect exactly once…we say they are CONSISTENT and INDEPENDENT

2. They will never intersect; they’re parallel or have the same slope (m) but different y intercepts (b)…we say they are INCONSISTENT

3. They will intersect infinitely, everywhere; they’re collinear or the same line. They have the same slope AND the same y intercept…we say they are CONSISTENT and DEPENDENT

We’ll graph two lines today and find the intersection point graphing by hand and on during this week on the graphing calculator.

The intersection coordinate is called the “SOLUTION OF THE SYSTEM.”

that is, x marks the spot ;)

You can check your coordinates by plugging them into both equations and make sure they work.

(or you can check on the graphing calculator by using the intersection app or the TABLE function to see that for the same x, they both have the same y value).