Question

In the following exercises, graph by plotting points.

$y=-2x+2$

Short answer

The graph of the equation is

Step-by-step solution

Step 1. Given Information

Given equation is$y=-2x+2$

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 $x=0$:

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

Plugging $x=1$:

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

Plugging $x=2$:

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

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

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