Chapter 8.3, Problem 14PPS

To determine

To calculate:To complete the below table and find four solutions for the below equation and to write the solutions as ordered pair −

  $y=5x+1$

$x$	$y=5x+1$	$y$
$-2$
$-1$
$0$
$1$

Answer to Problem 14PPS

The completed table is :

$x$	$y=5x+1$	$y$
$-2$	$y=5\left(-2\right)+1$	$-9$
$-1$	$y=5\left(-1\right)+1$	$-4$
$0$	$y=5\left(0\right)+1$	$1$
$1$	$y=5\left(1\right)+1$	$6$

Thus, the four ordered pairs are $\left(-2,-9\right)$ , $\left(-1,-4\right)$ , $\left(0,1\right)$ and $\left(1,6\right)$ .

Explanation of Solution

Given information:

Equation is $y=5x+1$

Formula Used:

To solve an equation with multiple variables, we need to consider some random values for one of the variables and solve for the other one to find the ordered pair.

Calculation:

Given equation is $y=5x+1$

Using the above explanation, we have -

Let the value of $x$ be $-2$ , substituting the value of $x$ in the above equation, we have:

  $y=5\left(-2\right)+1$

Solving the above equation, we have :

  $\begin{array}{l}y=-10+1\\ y=-9\end{array}$

Thus, the first ordered pair is $\left(-2,-9\right)$ .

Using the same approach to find the other ordered pairs −

Let the value of $x$ be $-1$ , substituting the value of $x$ in the above equation, we have:

  $y=5\left(-1\right)+1$

Solving the above equation, we have :

  $\begin{array}{l}y=-5+1\\ y=-4\end{array}$

Thus, the second ordered pair is $\left(-1,-4\right)$ .

Let the value of $x$ be $0$ , substituting the value of $x$ in the above equation, we have:

  $y=5\left(0\right)+1$

Solving the above equation, we have :

  $\begin{array}{l}y=0+1\\ y=1\end{array}$

Thus, the third ordered pair is $\left(0,1\right)$ .

Let the value of $x$ be $1$ , substituting the value of $x$ in the above equation, we have:

  $y=5\left(1\right)+1$

Solving the above equation, we have :

  $\begin{array}{l}y=5+1\\ y=6\end{array}$

Thus, the fourth ordered pair is $\left(1,6\right)$ .

The completed table is :

$x$	$y=5x+1$	$y$
$-2$	$y=5\left(-2\right)+1$	$-9$
$-1$	$y=5\left(-1\right)+1$	$-4$
$0$	$y=5\left(0\right)+1$	$1$
$1$	$y=5\left(1\right)+1$	$6$

Thus, the four ordered pairs are $\left(-2,-9\right)$ , $\left(-1,-4\right)$ , $\left(0,1\right)$ and $\left(1,6\right)$ .