Chapter 8.5, Problem 25SR

To determine

To find: four solutions and write the solutions as ordered pairs.

Answer to Problem 25SR

The solution of the equation in ordered pairs are:

  $(-1,-\frac{1}{2}),(0,0),(1,\frac{1}{2}),(2,1)$

Explanation of Solution

Given: $y=\frac{1}{2}x$

Calculation:

Consider the equation:

  $y=\frac{1}{2}x\mathrm{..........}(1)$

The objective is to find four solutions of the above equation and to write the solutions in ordered pairs.

First, choose four values for $x$ . Then substitute each value into the equation $(1)$ and solved for $y$ .

For $x=-1,$ the value of $y$ will be:

  $\begin{array}{l}y=\frac{1}{2}x\\ y=\frac{1}{2}\times (-1)[Substitutex=-1]\\ y=-\frac{1}{2}[Simplify]\end{array}$

Therefore, the solution is:

  $(-1,-\frac{1}{2})$

For $x=0$ , the value of $y$ will be:

  $\begin{array}{l}y=\frac{1}{2}x\\ y=\frac{1}{2}\times \left(0\right)[Substitutex=0]\\ y=0[Simplify]\end{array}$

Therefore, the solution is:

  $(0,0)$

For $x=1$ , the value of $y$ will be:

  $\begin{array}{l}y=\frac{1}{2}x\\ y=\frac{1}{2}\times \left(1\right)[Substitutex=1]\\ y=\frac{1}{2}[Simplify]\end{array}$

Therefore, the solution is:

  $(1,\frac{1}{2})$

For $x=2$ , the value of $y$ will be:

  $\begin{array}{l}y=\frac{1}{2}x\\ y=\frac{1}{2}\times \left(2\right)[Substitutex=2]\\ y=1[Simplify]\end{array}$

Therefore, the solution is:

  $(2,1)$

Conclusion:

Therefore, the solution of the equation in ordered pairs are:

  $(-1,-\frac{1}{2}),(0,0),(1,\frac{1}{2}),(2,1)$