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Relationship between two variables

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Relationship Between Two Variables

A relationship between two variables describes how one quantity (the dependent variable) changes as another (the independent variable) changes. Learn to record a relationship in a table of x and y values, plot it as a graph, and read it in both directions.

What a relationship between two variables is

A relationship between two variables describes how one quantity changes in connection with another. If you know the value of one variable, the relationship tells you what the other becomes. The variable you choose is called the independent variable (usually x); the variable that responds to it is the dependent variable (usually y).

A table of paired x and y values is the simplest way to record a relationship. For y = 2x, doubling each x-value gives its matching y-value: x = 1 gives y = 2, x = 2 gives y = 4, and so on.

A relationship between two variables: y = 2x A table lists x-values -2, -1, 0, 1, 2 with matching y-values -4, -2, 0, 2, 4 for the relation y = 2x. The points are plotted and connected as a straight line, showing that y depends on x. xy = 2x -2-4-1-2001224 x y
The table for y = 2x, with the paired values plotted as a straight line.

Plotting each (x, y) pair from the table as a point, then connecting the points, turns the table into a graph. When the points fall on a straight line, as they do for y = 2x, the relationship is linear. This is the same idea used when you graph using a table of values.

A relationship works in both directions: given an x-value you can find y, and given a y-value you can work backward to find x. This connects directly to x- and y-intercepts, which are just the special points where the line crosses each axis, and to identifying one-to-one functions, where every y-value traces back to exactly one x.

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