Chapter 1.3, Problem 47STP

To determine

Which rule describes the ordered pairs.

Answer to Problem 47STP

  $y=3x-2$

Explanation of Solution

Given:

The ordered pair is

X	y
1	1
2	4
3	7
4	10

  $\begin{array}{l}\text{F}\text{.y}=x\text{H}\text{.}y=3x-2\\ \text{G}\text{.}y=2x\text{J}\text{.}y=2x+2\end{array}$

In order to find which rule describes the ordered pairs

X	y
1	1
2	4
3	7
4	10

First checking the options by putting the values given in the table the expression option H in the correct answer as shown below:

  $\text{H}\text{.}y=3x-2$

Putting the value of x=1 in the expression

  $\begin{array}{l}\text{H}\text{.}y=3x-2\\ y=3x-2\\ y=3\cdot 1-2\\ y=1\end{array}$

Putting the value of x=2 in the expression

  $\begin{array}{l}\text{H}\text{.}y=3x-2\\ y=3\cdot 2-2\\ y=4\end{array}$

Putting the value of x=3 in the expression

  $\begin{array}{l}\text{H}\text{.}y=3x-2\\ y=3x-2\\ y=3\cdot 3-2\\ y=7\end{array}$

Putting the value of x=4 in the expression

  $\begin{array}{l}\text{H}\text{.}y=3x-2\\ y=3x-2\\ y=3\cdot 4-2\\ y=10\end{array}$

So, option H is the correct expression for the ordered pairs.