Graph 6x+3y=12

$6 x + 3 y = 12$

Step 1

Solve for $y$ .

Subtract $6 x$ from both sides of the equation.

$3 y = 12 - 6 x$

Divide each term in $3 y = 12 - 6 x$ by $3$ and simplify.

Divide each term in $3 y = 12 - 6 x$ by $3$ .

$\frac{3 y}{3} = \frac{12}{3} + \frac{- 6 x}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{12}{3} + \frac{- 6 x}{3}$

Divide $y$ by $1$ .

$y = \frac{12}{3} + \frac{- 6 x}{3}$

Simplify the right side.

Simplify each term.

Divide $12$ by $3$ .

$y = 4 + \frac{- 6 x}{3}$

Cancel the common factor of $- 6$ and $3$ .

Factor $3$ out of $- 6 x$ .

$y = 4 + \frac{3 (- 2 x)}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$y = 4 + \frac{3 (- 2 x)}{3 (1)}$

Cancel the common factor.

$y = 4 + \frac{3 (- 2 x)}{3 \cdot 1}$

Rewrite the expression.

$y = 4 + \frac{- 2 x}{1}$

Divide $- 2 x$ by $1$ .

$y = 4 - 2 x$

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 $4$ and $- 2 x$ .

$y = - 2 x + 4$

Step 3

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

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

$m = - 2$

$b = 4$

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

Slope: $- 2$

y-intercept: $(0, 4)$

Slope: $- 2$

y-intercept: $(0, 4)$

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 $4$ and $- 2 x$ .

$y = - 2 x + 4$

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

$\begin{array}{c} x & y \\ 0 & 4 \\ 1 & 2 \end{array}$

Step 5

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

Slope: $- 2$

y-intercept: $(0, 4)$

$\begin{array}{c} x & y \\ 0 & 4 \\ 1 & 2 \end{array}$

Step 6

Graph 6x+3y=12

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