Graph x>=-3y+6

$x \geq - 3 y + 6$

Step 1

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

Solve for $y$ .

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

$- 3 y + 6 \leq x$

Subtract $6$ from both sides of the inequality.

$- 3 y \leq x - 6$

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

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

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Divide $- 6$ by $- 3$ .

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

Reorder terms.

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

Remove parentheses.

$y \geq - \frac{1}{3} x + 2$

Step 2

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

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

$m = - \frac{1}{3}$

$b = 2$

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

Slope: $- \frac{1}{3}$

y-intercept: $(0, 2)$

Slope: $- \frac{1}{3}$

y-intercept: $(0, 2)$

Step 3

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $- \frac{1}{3} x + 2$ .

$y \geq - \frac{1}{3} x + 2$

Step 4

Graph x>=-3y+6

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