How to Identify Linear Functions by ordered pairs
Identifying a linear function by ordered pairs.
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This is just like using tables, with the only difference is you will have to put your ordered pairs into tables. If your values are in a table you can determine whether or not the data is linear if a constant change in x-corresponds to a constant change in y. However, you need to be careful if you find a constant change in the y-values, check for a constant in the x-values. Both need to be constant for the function to be linear. Sometimes test questions try to trick to you by making either the x or the y constant, but not the other. You can also plot the points in the tables in they form a straight line then it is a linear function.
Write the ordered pairs in a table, and look for patterns. If there is a constant change in x and a constant change in y then it is a linear function. Also, you can plot the points and graph.
(-2, 7), (-1, 4), (0, 4), (1, -2), (2, -5) | (-2, 6), (-1, 3), (0, 2), (1, 3), (2, 6) | |||
x | y | x | y | |
-2 | 7 | -2 | 6 | |
-1 | 4 | -1 | 3 | |
0 | 1 | 0 | 2 | |
1 | -2 | 1 | 3 | |
2 | -5 | 2 | 6 | |
In this table, a constant change of +1 in x-corresponds to a constant change of -3 of in y. These points satisfy a linear function. | In this table, a constant change of +1 in x does not correspond to a constant change in y. These points do not satisfy a linear function. | |||
Click here to learn about a standard form of a linear
equationTopics in this SectionIdentifying a linear function by its graph Identifying a linear function by tables Identifying a linear function by ordered pairs Standard form of a linear equations Finding x and y intercepts and using them to graph Arithmetic Sequence |