Algebra 1H Glencoe McGraw-Hill J. Evans/C. Logan
3-A5 Linear Functions
Graphing Using a Table of Values
In Chapter 2 you solved linear equations. In a linear equation the
exponent of the variable is one.
4012x 1
In this lesson you will graph linear equations in two variables. In a linear equation with two variables the exponent
of the variables is one (or zero).
4yx 1 1
In this lesson the equations will each have TWO VARIABLES, x and y
The graph of a linear equation is the
collection of all points (x, y) that are
SOLUTIONS of the equation. How many
points will the graph of a line contain? Way too many points to list.
1. Make a table of values (using advantageous x-values).
2. Graph enough points from the table to recognize a pattern.
3. Connect the points to form a line.
y
x
Ex. 1: Graph y = 2x + 3 by constructing a table of
values and graphing the solutions. Describe the
pattern you notice.
x y
-3
-2
-1
0
1
y = 2(-3) + 3
= -3-3
-1
1
3
5
The pattern? The points all lie on a line. The ENTIRE line, even the parts not
shown, is the graph of y = 2x + 3. Every point on the
line is a solution to the equation y = 2x + 3.
( )
( )
( )
( )
( )
Before sketching a graph, make sure your equation is in “function form”.
In function form, the y is isolated, making it much easier to construct a table of values.
Ex. 2: 4 2 2x y 4 4x x
2x4y2
2 2 2
2 4 2y x
1x2y
Think of an equation in function form as a type of machine……a function machine.
Input the x
y is the output
The function machine changes numbers. The input (the x value) enters the function machine and the function
produces an output (the y value).
1x2y 7
53
1
13
x y
-3
-2
-1
0
1
2
7y
Substitute the x values to find the corresponding values for
y.
1)3(2y 16y
1
3
x y y
x
-3
-2
-1
0
1
2
7
5
3
1
1Ex. 3: 3
2y x
5
4
3
2
1
x y
-4
-2
0
2
4
5y
32y
3)4(21
y
What x values should you choose?
y
x
5
4
3
2
1
x y
-4
-2
0
2
4
5x4y
3
1
5
9
13
x y
-2
-1
0
1
2
3y
58y
5)2(4y
5x4y
What do you need
to do first?
3
1
5
9
13
-2
-1
0
1
2
y
x
x y
(2, 13) will be off the graph. Four points should be
sufficient.
Important!!
When you plot the points on the graph they should lie in a straight line. These are linear
equations.
If the points you plot don’t lie in a straight line you have either made an arithmetic mistake
when you substituted in the x values -or-
you have plotted the points incorrectly!
Check your work to find the mistake—don’t draw a crooked line!
No graphs will be accepted if they have not been neatly and carefully
drawn on graph paper with a straight edge.
This is non-negotiable!