Page 192 - ABCTE Study Guide_Neat

Linear-Function Rule

Linear-function rules, which are also called linear equations, can be written from looking at
the x and y values given in a table. Writing function rules is really the same process as figuring out the
rule for any pattern.

For example, in a pattern written like this: 3, 7, 11, 15, 19, . . . , you figure out by trial and error that it
seems to work if you add four to get to the next number.

With linear functions, the rule could be slightly more complicated than x + 4 (although not always!), but if
you know the table is showing a linear function, then you also know that x can't be raised to any power
except one. (You just learned how to determine if the function is linear by looking at constant rate of
change; sometimes the problem will just state for you that the function is linear.)

The rate of change comes in handy another way. The rate of change is the number by which x is
multiplied in the function rule. Then figure out what to add or subtract to get to the number in the y-value
column. It should be the same number each time as you move through the table.

You can try the guess-and-check method first; you can often come up with the rule fairly easily on your
own, especially if x is not multiplied by a fraction.

Let's take a look at a few examples. Write the function rule for each linear function.

Question

Which linear-function rule correctly represents the data in the table below?

x y
-2 -7

0 -1

1 2

4 11

A y = x - 1

B y = 2x + 3