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!