Exponents        Single Var. Eq.        Multi-Var. Eq.        Word Problems        Factoring        Fractions        Ratios        Number Lines    Coordinate Plane       Square Roots        Scientific Not. 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. 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. ``` 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. 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!

Math for Morons Like Us - Algebra: Graphing on the Coordinate Plane
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