Chapter 4.3, Problem 1STP

For Exercises $1-5,$ choose the correct letter.

Which ordered pair represents a linear function?

A. $(-2,-15),(-1,-9),(0,-3),(1,3),$ and (2,9)

B. $(-2,4),(-1,1),(0,0),(1,1),$ and (2,4)

C. (-2,-1),(-1,-4),(0,-5),(1,-4) and (2,-1)

D. $(-2,-8),(-1,-1),(0,0),(1,1),$ and (2,8)

To determine

To select the order pair that represents a linear function.

Answer to Problem 1STP

A.) $\left(-2,-15\right),\left(-1,-9\right),\left(0,-3\right),\left(1,3\right)and\left(2,9\right).$

Explanation of Solution

Given information:

Given options

  $A).\left(-2,-15\right),\left(-1,-9\right),\left(0,-3\right),\left(1,3\right)and\left(2,9\right)$

  $B.)\left(-2,4\right),\left(-1,1\right),\left(0,0\right),\left(1,1\right)and\left(2,4\right)$

  $C.)\left(-2,-1\right),\left(-1,-1\right),\left(0,0\right),\left(1,1\right)and\left(2,8\right)$

  $D.)\left(-2,-8\right),\left(-1,-1\right),\left(0,0\right),\left(1,1\right)and\left(2,8\right)$

In order to be a linear function, a set of ordered pair must have a constant rate of change.

In the given order pairs in all options, x -coordinate values are {-2,-1,0,1,2}.

Differences of x -coordinate values of ordered pairs in all options is 1.

But only the differences of y -coordinate values of ordered pairs in option A is constant.

It can be seen that

  $\begin{array}{l}-9-\left(-15\right)=-9+15=6\hfill \\ -3-\left(-9\right)=-3+9=6\hfill \\ 3-\left(-3\right)=3+3=6\hfill \\ 9-3=6\hfill \end{array}$

This shows a constant rate of change of 6.

So, the correct answer is

A.) $\left(-2,-15\right),\left(-1,-9\right),\left(0,-3\right),\left(1,3\right)and\left(2,9\right).$