In this video we’re going to look at how to use substitution in equations to generate a table of ordered pairs. Ordered pairs (coordinates) can be used to solve equations, to plot graphs, and so we come across them a lot in Maths.
You should already know how to substitute into equations, and how to solve simple equations. We have this relationship y = 3x + 1. The value of ‘y’ depends on what the value of ‘x’ is. So if ‘x’ is 2, then y is 7. This can be written an (2, 7). We can generate a table of values by substituting in different values of 'x' and finding the corresponding 'y' values.
Once we've generated a table of values, we can then write out the values as ordered pairs: (0, 1) (1, 4) (2, 7) (3, 10). Always write the ‘x’ value before the ‘y’ value (x, y) and not (y, x). The ‘x’ and ‘y’ are both known as variables, because they aren’t set values. They vary. Even more specifically, we call the ‘x’ the INDEPENDENT variable, because we can choose any value of ‘x’ randomly or independently. But the ‘y’ is known as the ‘DEPENDENT’ variable. Y depends upon the value of ‘x’.
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