Q5A. - Algebra 1

Question

Graph each equation by making a table.

$2x-y=2$.

Step-by-Step Solution

Answer

The table of values for the points $\left(x,y\right)$ is:

$x$	$y$	$\left(x,y\right)$
0	$-2$	$\left(0,-2\right)$
1	0	$\left(1,0\right)$
$\frac{1}{2}$	$-1$	$\left(\frac{1}{2},-1\right)$
2	2	$\left(2,2\right)$

The graph of the equation $2x-y=2$ is:

Step 1. Find the values of y for some values of x .

Find the value of $y$ for $x=0$.

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

 

Find the value of $y$ for $x=1$.

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

 

Find the value of $y$ for $x=\frac{1}{2}$.

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

 

Find the value of $y$ for $x=2$.

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

Step 2. Make a table of values for the points x , y .

The table of values for the points $\left(x,y\right)$ is:

$x$	$y$	$\left(x,y\right)$
0	$-2$	$\left(0,-2\right)$
1	0	$\left(1,0\right)$
$\frac{1}{2}$	$-1$	$\left(\frac{1}{2},-1\right)$
2	2	$\left(2,2\right)$

Step 3. Graph the equation 2 x − y = 2 .

The plot of the points $\left(x,y\right)$ is:

Draw the graph of the equation $2x-y=2$ by joining the plotted points.

Therefore, the graph of the equation width="69" style="max-width: none; vertical-align: -4px;" $2x-y=2$ is: