Linear Functions

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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 equation

Topics in this Section

Identifying 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

Rate of change slope

Describing Slope

The Slope Formula

Direct Variation

Arithmetic Sequence

Slope-Intercept Form

Point-Slope Form

Slopes of Parallel and Perpendicular Lines

Forms of the Equation of a Line