How to Learn Math's Point System
Learning how to interpret and use the coordinate plane or "point system" is one of the trickiest hurdles in introductory algebra. You must understand the quadrants and be able to plot points before moving on to graphing equations and other more advanced skills. Although the coordinate plane may seem complicated, its visual nature actually makes it a very straightforward method for conveying algebraic information.
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Instructions
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1
Review the integer number line that you may have learned in an earlier class or chapter. This line starts with a zero in the middle and extends to the right with increasing positive numbers and to the left with decreasing negative numbers. The line is often labeled with each individual integer (... -2, -1, 0, 1, 2...) or with integers by a scale of 2s or 5s.
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Practice plotting integers, decimals and fractions on the line as dots. For instance, you would draw 3.2 a little bit to the right of the "3" mark and to the left of the "4" mark, while -4.5 would lie between -4 and -5. The coordinate plane uses the same plotting concept and labeling system.
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Draw a cross about 2 inches wide and 2 inches long, using the lines of the graphing paper as a guide. The horizontal line is called the "x-axis" and works just like the number line. The vertical line is called the "y-axis" and also works like the number line except that it goes up and down instead of across (the smaller a number, the lower down you would plot it). The point where the two lines cross is called the "origin." This is "zero" for both the horizontal x-axis and the vertical y-axis.
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Draw a notch mark at each point where a graphing paper line crosses with the x-axis. Do the same for the y-axis. If it helps you, label each of these marks with the appropriate integer. Stick with individual integers at first because scales will make the point system more difficult to learn.
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Look at the point you need to plot. It should be in parentheses with a comma between two numbers, e.g., (-2,3). This is called an "ordered pair." The first number refers to the x-axis and tells you how far to move left or right from zero. Place your pencil (without making a mark) on zero, then move it the appropriate number of spaces left or right just as you would on the number line. In this case, you would move 2 to the left.
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Use the second number in the parentheses to determine how far to move up or down. Start your pencil on the spot where you landed when moving left or right, then move your pencil up or down the correct number of spaces from there. For the ordered pair (-2, 3), you would move three spaces up. Use the notches on the y-axis (the vertical line) to help you count.
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Draw a dot where you landed after having moved back/forth and up/down. You should not have made any marks up until this point.
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Copy the parentheses and the ordered pair in the space next to the dot.
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Tips & Warnings
The four "sections" formed by the cross of the coordinate plane are called quadrants and are named in counterclockwise order, starting with quadrant I in the upper right.
You can predict which quadrant an ordered pair will fall in based on the signs of its numbers: quadrant I (+,+), quadrant II (-,+), quadrant III (-,-), and quadrant IV (+,-).
