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# Graphing Linear Equations using Table of values - PowerPoint PPT Presentation

Graphing Linear Equations using Table of values. Graphing Using a Table of Values. A table of values is a list of numbers that are used to substitute one variable, to find the value of the other variable, or missing number. Each row in a table of values represents a coordinate on the line.

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Graphing Linear Equations using Table of values

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## Graphing Linear Equations using Table of values

### Graphing Using a Table of Values

• A table of values is a list of numbers that are used to substitute one variable, to find the value of the other variable, or missing number.

• Each row in a table of values represents a coordinate on the line.

• If you are asked to graph a relationship based on its equation, a table of values forms a set of ordered pairs that can be plotted.

### Table of Values:

• Choose x-values (e.g. –2, –1, 0, 1, 2)

• Calculate y-values

• Ex.

5

(–2, 5)

3

(–1, 3)

1

(0, 1)

-1

(1, –1)

-3

(2, –3)

### Graphing the Table of Values

• Plot the points

• Draw a line through

• Place arrows on ends

• Label

y

(–2, 5)

(–1, 3)

x

(0, 1)

(1, –1)

(2, –3)

### Table of Values:

• Choose x-values

• Calculate y-values

• Ex.

-2

(–2, –2)

1

(–1, 1)

4

(0, 4)

7

(1, 7)

10

(2, 10)

### Graphing the Table of Values

• Plot the points

• Draw a line through

• Place arrows on ends

• Label

y

(–2, -2)

(–1, 1)

x

(0, 4)

(1, 7)

(2, 10)

### More Examples

Create a table of values and a graph for each situation below.

a) To hold a banquet, it costs \$150 to rent the hall, plus \$25 for every person attending

### Graph

300

275

250

225

200

175

150

1 2 3 4 5 6 7 8

Number of People Attending

## Linear vs. Non-linear RelationsANDFirst Differences

• A linear relation is a relationship between two variables where when you plot their values on a coordinate system, you get a straight line

• A linear relation may be modeled in 3 ways:

An equationA table of valuesA graph

y

(–2, -2)

(–1, 1)

(0, 4)

x

(1, 7)

(2, 10)

### First Differences

• First differences allow you to determine whether a relationship is linear or non-linear, without having to graph the data.

LINEAR

NON LINEAR

• The x-values must be consecutive.

• In other words, they must increase by the same amount

• If the relationship is linear – the first differences will be the same!!

• Determine if the following relationships are linear or non-linear.

• First differences are the same…LINEAR

5 – 1 = 4

9 – 5 = 4

13 – 9 = 4

17 – 13 = 4

• Determine if the following relationships are linear or non-linear.

• First differences are the NOT the same…

• NON-LINEAR

8 – 16 = -8

4 – 8 = -4

2 – 4 = -2

1 – 2 = -1

### Home Work

• Page 8 and 9 (All Questions)

• Page 10 (Question 10 only)