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Graphing Linear Equations using Table of valuesPowerPoint Presentation

Graphing Linear Equations using Table of values

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### Graphing Linear Equations using Table of values

### Linear vs. Non-linear RelationsANDFirst Differences

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

- 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 equation A table of values A 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 non-linear.

- Page 8 and 9 (All Questions)
- Page 10 (Question 10 only)

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