Graph the pair of equations $y=-\frac{1}{2}x$and $y=-\frac{1}{2}$in the same rectangular coordinate system.

A pair of equations$y=-\frac{1}{2}x$and$y=-\frac{1}{2}$is given.

First take $x=0$and solve for $y$as shown below:

$$\begin{gathered} y=-\frac{1}{2}\left(0\right) \\ y=0 \end{gathered}$$

Next take $x=2$and solve for $y$as shown below:

$$\begin{gathered} y=-\frac{1}{2}\left(2\right) \\ y=-1 \end{gathered}$$

At last take $x=4$and solve for $y$as:

$$\begin{gathered} y=-\frac{1}{2}\left(4\right) \\ y=-2 \end{gathered}$$

Thus the three ordered pairs are$(0,0),(2,-1),(4,-2)$.

The equation $y=-\frac{1}{2}$is a horizontal line of the form $y=b$passing through the y-axis at $(0,b)$. The equation $y=-\frac{1}{2}$has only one variable $y$and the value of $y$is constant.

The graph of equation $y=-\frac{1}{2}$is a horizontal line passing through the y-axis at$-\frac{1}{2}$.

The tables are created using ordered pairs as shown below:

Both equations are plotted on same rectangular coordinate system by plotting the points from the tables and drawing the lines joining the points in the graph as shown below: