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 increase or decrease steadily. Look at the following function and table of
points from the function:
Y = 4 * X + 2
Now, answer some questions for me. What is the value of the function when X is 0?
Mentor: Good. What is the change in the value of the function as X increases by 1?
Student: Well, the value of the function goes from 2 to 6 to 10. So at each step the function
increases by 4.
Mentor: Now look at your answers: 2 for the starting point, when X is 0 and 4 for the increase. Do
those numbers look familiar?
Student: In the original function, Y = 4 * X + 2, m = 4 and b = 2. The same numbers we got for the
starting value and the increasing value. Is this a coincidence?
Mentor: No, it is not a coincidence. This always works. Try some.
Student: Here are a few:
Y = 10 * X - 1
Change = 10, start = -1
Y = -2 * X + 3
Change = -2, start = 3
Y = 5 * X + 11
Change = 5, start = 11
Mentor: Good! But before we begin, 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? You may wish
Simple Plot to plot the ordered pairs from your table.