University:
University of Houston
Course:
MATH 3311 | Functions and Modeling
Academic year:

2024
Views:

235

Pages:

5
Author:

Braelyn Harmon

A table of data is linear if there is a constant average rate of change between all pairs of points. Testing for Linearity • to test if a table of data is linear, calculate the average rate of change between each consecutive pair of points • if the rate of change is constant, the data represents a linear function • if not, then it is not a linear function x 0 2 5 9 y 0 64 160 288 x 3 4 6 9 y 4 6 10 18 Example 1 Determine whether or not each of the following tables represents a linear function. (a) x 2 4 6 8 y 12 17 21 25 (b) x 0 3 5 6 9 y 4 13 19 22 31 Finding a Formula for a Table that is Linear • the constant average rate of change found when determining that the table is linear is the slope of the line • use this slope and any one point from the table, write the equation using the pointslope form, then solve for “y” to get the function equation Continuing our earlier example: x 0 2 5 9 y 0 64 160 288 Example 2 Show that the table represents a linear function and then give a formula for the function. x 2 5 7 12 y 8.5 15.7 20.5 32.5 Example 3 The table below shows the cost C, in dollars, for a company to produce n widgets. Show that table is represents a linear function, find the formula for this function, and then represent in function notation the cost to produce 875 widgets. n 200 250 300 350 C 7900 9650 11400 13150 Plotting a Table of Data We will walk through plotting the data from the first example. Press Press Press x 0 2 5 9 y 0 64 160 288 , select Plot1, turn the plot on, choose scatterplot, set Xlist and Ylist , choose “EDIT”, put the x-values in L1 and the y-values in L2 to see the scatterplot Example 4 Plot each of the following tables of data. Does the plot look linear? (a) x 1.3 2.5 3.3 4.2 5.1 y 2.6 2.3 2 1.8 1.5 x 0.3 1.3 2.2 3.3 4.1 y 5.6 2 0.92 0.77 0.51 (b)

Modeling Data With Linear Functions

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