Graph 3x-2y>6

$3 x - 2 y > 6$

Step 1

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

Solve for $y$ .

Subtract $3 x$ from both sides of the inequality.

$- 2 y > 6 - 3 x$

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

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

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $6$ by $- 2$ .

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

Dividing two negative values results in a positive value.

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

Rearrange terms.

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

Reorder terms.

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

Step 2

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

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

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

$b = - 3$

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

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

y-intercept: $(0, - 3)$

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

y-intercept: $(0, - 3)$

Step 3

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

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

Step 4

Graph 3x-2y>6

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