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Algebra 1H Glencoe McGraw-Hill J. Evans/C. Logan

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3-A5 Linear Functions

Graphing Using a Table of Values

Algebra 1H Glencoe McGraw-Hill J. Evans/C. Logan

In Chapter 2 you solved linear equations. In a linear equation the exponent of the variable is one.

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).

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.

- Make a table of values (using advantageous x-values).

- Graph enough points from the table to recognize a pattern.

3. Connect the points to form a line.

Ex. 1: Graph y = 2x + 3 by constructing a table of values and graphing the solutions. Describe the pattern you notice.

y

x

y = 2(-3) + 3

= -3

x y

-3

-2

-1

0

1

( )

-3

( )

-1

( )

1

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.

( )

3

( )

5

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.

Think of an equation in function form as a type of machine……a function machine.

The function machine changes numbers. The input(the x value) enters the function machine and the function produces an output (the y value).

Input thex

y is the output

xy

-3

-2

-1

0

1

2

Substitute the x values to find the corresponding values for y.

y

xy

-3

-2

-1

x

0

1

2

xy

-4

-2

0

2

4

What xvalues should you choose?

y

xy

-4

-2

0

x

2

4

xy

-2

-1

0

1

2

What do you need to do first?

x y

y

-2

-1

0

1

x

2

(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!