Putting it all together

Ms. Russell's Guides
Linear Functions

What is a Function? The Definition of a Line The Big Deal with Slopes How Can I remember? Putting It Together Quiz Yourself

Linear Functions Revisited

line

The equation we use to represent linear functions is:

y = mx + b

m is the slope
b is the y-intercept

line

Let's make this a little simpler.

Every line sits somewhere on the coordinate plane.
The number "b" tells us exactly where.

yintercept

"b" represents the y-value of the one point on the line that lays on the y-axis.

For this line, there would be a 1 in the place of the "b"
because the line touches the y-axis at the point (0,1)

The Slope of a line can be read between any two clear points on the graph.
The "m" tells us how steep the line is
and if it goes up or down.

slope

"m" is the slope and can be determined by counting the Rise and the Run between two points on the line.

For this line, the slope is
3/2 because from one point to the other it rises 3 and runs 2.

It is positive because it rises from left to right.

The equation of this linear function is
y = (3/2)x + 1.

So, really, there are only two pieces to this linear function puzzle:
1. "m" the slope
2. "b" the y-intercept

The Final Tie-In

Do you remember the function machine?

Whenever you put an "x" into the machine,
you will get only one "y".

Think, for example, about the line
y = 2x + 3

If I plug x=2 as the input, then the machine will give me y=7 as the output.
If I plug x=-4 as the input, then the machine will give me y=-5 as the output.
And so on.

What's key to remember here is that if a point is on the line,
it will show by substituting the x and y values into the equation.

(2,6) is not on the line because
6 is not 2(2) + 3

(12,27) is on the line because
27 = 2(12) + 3

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