Simple Equations - Algebra
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Simple Equations

simple equation
Graph of the equations y = 3 and x = 3

When we learn to add and subtract, multiply and divide, we think of numbers as being all along the number line. But in algebra we think about numbers as being in a plane. Picture two number lines crossing each other at zero. The one that goes up and down we call the y-axis and the one that goes from side to side we call the x-axis. The x-axis is always perpendicular to the y-axis - at right angles to it. All of the points on the plane can be described by naming a y number and an x number. So y=3, x=4 means you go up three and right four and make a point there. The negative numbers are down and to the left, so y = -3, x = -4 means you go down three and left four and make a point there.

The equation y = 3 means that you draw all of the points on the number plane where y is equal to 3. So you make a point where x = 0 and y = 3, and another point where x = 1 and y = 3, and another point where x = 2 and y = 3, and so on. That gives you a horizontal line, three numbers above zero.

The equation x = 3 means that you draw all of the points on the number plane where x is equal to 3. So you make a point where y = 0 and x = 3, and so on. That gives you a vertical line, three numbers to the right of zero.

Learn by doing - the number plane
More about geometry

Bibliography and further reading about algebra:

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Karen Carr is Associate Professor Emerita, Department of History, Portland State University. She holds a doctorate in Classical Art and Archaeology from the University of Michigan. Follow her on Instagram or Twitter.
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