Linear Functions

Here we are looking at the relationship of one set of values to another. We are asking the question, “If x is this, what is y?”. Since we only know what y is if we know what x is, we say that y depends on x, or y is the dependent variable and a x is the independent variable.

Here’s an easy example:

What is the relationship between the number of weeks that go by and the amount of pocket money you get? Here we are asking questions like “How much pocket money will I get over 3 weeks?”, “How much will I get over 7 weeks?” etc. Which is the independent variable and which is the dependent variable?

If you plot this information, with the independent variable on the x-axis and the dependent variable on the y-axis, you will see that the points form a straigh line. Relationships between two variables that form a straight line when you plot them on a graph are called Linear.

Not all relationships like this are linear. Try plotting a graph with the length of the side of a square on the x-axis, and the area of that square on the y-axis.

IM10L02 Review of Linear Relations


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