Question

In the following exercises, graph by plotting points.

$y=-x-3$

Short answer

The graph of the equation is

Step-by-step solution

Step 1. Given Information

Given equation is$y=-x-3$

The graph of the equation is to be determined plotting points.

Step 2. Find the points

A graph a linear equation two points are required and a third point would verify if the graph is correct i.e. if all the three lie on the same line then the graph is correct.

To determine the points, plugging x values and the corresponding y values are to be calculated.

Plugging $x=0$:

$$\begin{gathered} y=-x-3 \\ y=-0-3 \\ y=-3 \end{gathered}$$

Plugging $x=1$:

$$\begin{gathered} y=-x-3 \\ y=-1-3 \\ y=-4 \end{gathered}$$

Plugging $x=2$:

$$\begin{gathered} y=-x-3 \\ y=-2-3 \\ y=-5 \end{gathered}$$

Hence the points are$\left(0,-3\right),\left(1,-4\right),\left(2,-5\right)$

Step 3. Plotting the points

Plotting the points on the rectangular coordinate plane and joining them using a line:

Step 4. Conclusion

The graph of the equation by plotting points is