On this page, we hope to clear up problems that you might
have with graphing on the coordinate plane.
Coordinate planes are used extensively throughout
math and math related subjects (such as physics). They
are most useful when you need to graph an equation.
Scroll down or use the links below to start understanding
how to graph on the coordinate plane!
Graphing points
Graphing lines
Topics related to graphing
Quiz on Graphing on the Coordinate Plane
Because
graphing points on a coordinate plane is usually covered in the typical
pre-algebra course, we followed that tradition on this site.
You can click here to
better understand that area of graphing.
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In this
section we will help you understand how to graph lines
on a coordinate plane.
Most pre-algebra courses cover how to graph simple equations such as the
following: y = 2x + 1. So we followed the tradition on this site. You
can click here to better
understand that area of graphing.
In math, a line is defined to be of infinite length and consisting of
at least 2 points. All lines are straight (a line is
straight - a curve is curved).
When you need to graph an equation such as y = -(1/2)x + 2, the
only thing you need to be especially wary of is the fraction.
Since a line consists of two or more points, all you need to
do is find two or more ordered pairs that solve the equation.
The easiest way to do this is to draw a table such as the following and
fill it in:
---------
x | y
---------
0 |
2 |
4 |
You
plug the x-values into the equation and find the
y-values. That gives you ordered pairs that you can
graph on the coordinate plane and then "connect" into
a line.
1. Graph: y = -.5x + 2
Solution: Begin by making a table (choose convenient
values for x).
------------------
| x | 0 | 2 | -2 |
------------------
| y | | | |
------------------
Now plug the x-values into the original
equation and find the values for y.
y = -.5(0) + 2
y = 2
y = -.5(2) + 2
y = 1
y = -.5(-2) + 2
y = 3
Complete the table.
------------------
| x | 0 | 2 | -2 |
------------------
| y | 2 | 1 | 3 |
------------------
Now graph the points and draw a line by
"connecting the dots." (Aren't you overwhelmed
by all this fun?) Here's what it looks like:
The most
confusing types of lines are lines that are either
horizontal or vertical. These are
lines that are representative of an equation that has
either an x variable or a y variable, but not both.
An equation such as y = 2 says that no matter what you plug
in for y, you get 2.
An equation such as x = 4 has two things to keep in mind. First
of all, it has no slope! This is because it is vertical. (With a
horizontal line, the slope is zero, but with a vertical line, the slope
is undefined, so the line therefore has no slope.) The other thing to remember
is that no matter what you plug in for x, you'll get 4.
1. Graph: y = 2
Solution: This equation indicates that all
the y coordinates to be
graphed are 2. Pick any
two ordered pairs with 2 as
the y coordinate and graph.
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Below are a couple of
links to pages that discuss topics related to graphing, such as finding solutions to
systems of equations. They are not covered on this page in the spirit of
convenience. :-) If it's not convenient, you
could complain, and we might listen. :-)
Finding the solutions to systems of equations by graphing.
Writing the equation of the graph of a line.
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Take the Quiz
on graphing on the coordinate plane. (Very useful to review or to see if you've
really got this topic down.) Do it!
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