Graph 3x>=12-6y

$3 x \geq 12 - 6 y$

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

Solve for $y$ .

Rewrite so $y$ is on the left side of the inequality.

$12 - 6 y \leq 3 x$

Subtract $12$ from both sides of the inequality.

$- 6 y \leq 3 x - 12$

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

Divide each term in $- 6 y \leq 3 x - 12$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

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

Factor $3$ out of $3 x$ .

$y \geq \frac{3 (x)}{- 6} + \frac{- 12}{- 6}$

Cancel the common factors.

Factor $3$ out of $- 6$ .

$y \geq \frac{3 x}{3 \cdot - 2} + \frac{- 12}{- 6}$

Cancel the common factor.

$y \geq \frac{3 x}{3 \cdot - 2} + \frac{- 12}{- 6}$

Rewrite the expression.

$y \geq \frac{x}{- 2} + \frac{- 12}{- 6}$

Move the negative in front of the fraction.

$y \geq - \frac{x}{2} + \frac{- 12}{- 6}$

Divide $- 12$ by $- 6$ .

$y \geq - \frac{x}{2} + 2$

Reorder terms.

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

Remove parentheses.

$y \geq - \frac{1}{2} x + 2$

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

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

$m = - \frac{1}{2}$

$b = 2$

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

Slope: $- \frac{1}{2}$

y-intercept: $(0, 2)$

Slope: $- \frac{1}{2}$

y-intercept: $(0, 2)$

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $- \frac{1}{2} x + 2$ .

$y \geq - \frac{1}{2} x + 2$

Graph 3x>=12-6y

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