Question

In the following exercises, graph by plotting points.

$2x+y=7$

Short answer

The graph of the equation is

Step-by-step solution

Step 1. Given information

Equation to be plotted is

$2x+y=7$

It can be rewritten as

$y=7-2x$

Step 2. To find three points whose coordinates are solution to the equation     

When$x=0$

localid="1645013086203" $$\begin{gathered} y=7-2\times 0 \\ y=7 \end{gathered}$$

When$x=2$

localid="1645013059684" $$\begin{gathered} y=7-2\times 2 \\ y=7-4 \\ y=3 \end{gathered}$$

When $x=-2$

localid="1645013023422" $$\begin{gathered} y=7-2(-2) \\ y=7+4 \\ y=11 \end{gathered}$$

Now arrange these points in a table

x	y	(x,y)
0	7	(0,7)
2	3	(2,3)
-2	11	(-2,11)

Step 3. Plot these points in a rectangular coordinate system      

points(0,7), (2,3) and (-2,11) are plotted as

Step 4. Draw the line through three points and extend the line.    

The line is the graph of the equation