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).
