Graph 2x+3y=6

$2 x + 3 y = 6$

Step 1

Solve for $y$ .

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

$3 y = 6 - 2 x$

Divide each term in $3 y = 6 - 2 x$ by $3$ and simplify.

Divide each term in $3 y = 6 - 2 x$ by $3$ .

$\frac{3 y}{3} = \frac{6}{3} + \frac{- 2 x}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{6}{3} + \frac{- 2 x}{3}$

Divide $y$ by $1$ .

$y = \frac{6}{3} + \frac{- 2 x}{3}$

Simplify the right side.

Simplify each term.

Divide $6$ by $3$ .

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

Move the negative in front of the fraction.

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

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 $2$ and $- \frac{2 x}{3}$ .

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

Write in $y = m x + b$ form.

Reorder terms.

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

Remove parentheses.

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

Step 3

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

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

$m = - \frac{2}{3}$

$b = 2$

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

Slope: $- \frac{2}{3}$

y-intercept: $(0, 2)$

Slope: $- \frac{2}{3}$

y-intercept: $(0, 2)$

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.

Write in $y = m x + b$ form.

Reorder $2$ and $- \frac{2 x}{3}$ .

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

Reorder terms.

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

Remove parentheses.

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

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

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

Step 5

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

Slope: $- \frac{2}{3}$

y-intercept: $(0, 2)$

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

Step 6

Graph 2x+3y=6

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