Start by thinking of a number line
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.
What is algebra?
Medieval Islamic math
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Another number line crosses it
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.
What is a point?
Naming points on a plane
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. Where the two lines meet, that’s zero.
Who invented numbers?
Indian numbers and zero
An equation names a line
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.
What is a line?
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.
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