Graph 2x-3y>6

$2 x - 3 y > 6$

Step 1

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

Solve for $y$ .

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

$- 3 y > 6 - 2 x$

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

Divide each term in $- 3 y > 6 - 2 x$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

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 $- 3$ .

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

Dividing two negative values results in a positive value.

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

Rearrange terms.

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

Reorder terms.

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

Step 2

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 3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $\frac{2}{3} x - 2$ .

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

Step 4

Graph 2x-3y>6

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