Graph 2x+2y=6

$2 x + 2 y = 6$

Step 1

Solve for $y$ .

Subtract $2 x$ from both sides of the equation.

$2 y = 6 - 2 x$

Divide each term in $2 y = 6 - 2 x$ by $2$ and simplify.

Divide each term in $2 y = 6 - 2 x$ by $2$ .

$\frac{2 y}{2} = \frac{6}{2} + \frac{- 2 x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{6}{2} + \frac{- 2 x}{2}$

Divide $y$ by $1$ .

$y = \frac{6}{2} + \frac{- 2 x}{2}$

Simplify the right side.

Simplify each term.

Divide $6$ by $2$ .

$y = 3 + \frac{- 2 x}{2}$

Cancel the common factor of $- 2$ and $2$ .

Factor $2$ out of $- 2 x$ .

$y = 3 + \frac{2 (- x)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$y = 3 + \frac{2 (- x)}{2 (1)}$

Cancel the common factor.

$y = 3 + \frac{2 (- x)}{2 \cdot 1}$

Rewrite the expression.

$y = 3 + \frac{- x}{1}$

Divide $- x$ by $1$ .

$y = 3 - x$

Step 2

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Reorder $3$ and $- x$ .

$y = - x + 3$

Step 3

Use the slope-intercept form to find the slope and y-intercept.

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = - 1$

$b = 3$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $- 1$

y-intercept: $(0, 3)$

Slope: $- 1$

y-intercept: $(0, 3)$

Step 4

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

Reorder $3$ and $- x$ .

$y = - x + 3$

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & 3 \\ 1 & 2 \end{array}$

Step 5

Graph the line using the slope and the y-intercept, or the points.

Slope: $- 1$

y-intercept: $(0, 3)$

$\begin{array}{c} x & y \\ 0 & 3 \\ 1 & 2 \end{array}$

Step 6

Graph 2x+2y=6

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