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.

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Graphing Linear Equations using Table of values

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Graphing linear equations using table of values

Graphing Linear Equations using Table of values


Graphing using a 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

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

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 values1

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 values1

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)


Try these examples

Try these examples:


More examples

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

Graph

300

275

250

225

200

175

150

1 2 3 4 5 6 7 8

Number of People Attending


Linear vs non linear relations and first differences

Linear vs. Non-linear RelationsANDFirst Differences


Graphing linear equations using table of values

  • 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)


Which of the following is linear

WHICH OF THE FOLLOWING IS LINEAR!


First differences

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


Graphing linear equations using table of values

  • 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!!


Graphing linear equations using table of values

  • 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


Graphing linear equations using table of values

  • 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

Home Work

  • Page 8 and 9 (All Questions)

  • Page 10 (Question 10 only)


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