Student: So I have practiced guessing functions and am geting pretty good at it as long as there is one operation. The more complicated functions are harder.

Mentor: Yes, they are. The best way to understand such functions is to study one kind at a time. Let's start with functions of the form:

These functions are called linear functions, and are often written as:

Where m represents the number multiplied to X and b represents the number added to the result.

Student: What's so important about these?

Mentor: These functions represent things that increase or decrease steadily. Look at the following function and table of points from the function:

Where does this function "Start" by which I mean what is Y when X is zero?

Student: 2.

Mentor: Good. What is the change in the function for each step?

Student: Do you mean as X gets bigger by 1?

Mentor: Yes.

Student: Well, if goes from 2 to 6 - which is a change of 4; then from 6 to 10 - which is a change of 4; and then from 10 to 14 --- Oh, I get it! The change is 4! So, the number multiplied is the change and the number added is the start.

Mentor: Exactly! This always works. Try some.

Student: Here are a few:

Mentor: Good! Let's get the terminology right: The change is called the slope and the starting value is called the intercept. We'll learn why these words are used later when we talk about graphs. Can you build a few tables of ordered pairs to further demonstrate these facts about your functions?

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