09 - First Differences - Notes PDF

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9 - First Differences

MPM1D – Linear Relationships

Date: ____________________________________________

First Differences Consider the relation  = 2 Complete the following table of values. Then graph the relation on the graph provided. x

y

0

0

2

4

4 6 8 10

Is the above relation linear or non-linear? ___________________________________ Describe the pattern on the x values. ____________________________________________________ Describe the pattern on the y values. ____________________________________________________ First differences are calculated by determining the difference between two consecutive, evenly spaced y-values in a table of values. Complete the following table by calculating the first differences:

What do you notice about the first differences? ________________________________

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9 - First Differences

MPM1D – Linear Relationships

Consider the relation:  =   . Complete the following table of values. Then graph the relation on the graph provided. x

y

0

0

1

1

2 3 4

Is the above relation linear or non-linear? _______________________________________ Describe the pattern on the x values. _________________________________________________ Describe the pattern on the y values. _________________________________________________ Complete the following table by calculating the first differences:

What do you notice about the first differences? ______________________________________________

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9 - First Differences

MPM1D – Linear Relationships

Summary •

First Differences are the differences between consecutive (one after another) y-values in a table of values with evenly spaced x-values.

•

To find first differences, we subtract the consecutive y-values working from the bottom up towards the top

Conclusion: If the first differences are constant, the relation is

___________________________________

If the first differences are not constant, the relation is

___________________________________

Examples: Calculate the first differences for the following relations and then classify them as linear or non-linear.

______________________________________

______________________________________

Homework Page 275 Questions C1, 1, 2, 4, 5

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