Graph 9x+3y-6<=0

$9 x + 3 y - 6 \leq 0$

Step 1

Solve for $y$ .

Move all terms not containing $y$ to the right side of the inequality.

Subtract $9 x$ from both sides of the inequality.

$3 y - 6 \leq - 9 x$

Add $6$ to both sides of the inequality.

$3 y \leq - 9 x + 6$

Divide each term in $3 y \leq - 9 x + 6$ by $3$ and simplify.

Divide each term in $3 y \leq - 9 x + 6$ by $3$ .

$\frac{3 y}{3} \leq \frac{- 9 x}{3} + \frac{6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} \leq \frac{- 9 x}{3} + \frac{6}{3}$

Divide $y$ by $1$ .

$y \leq \frac{- 9 x}{3} + \frac{6}{3}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 9$ and $3$ .

Factor $3$ out of $- 9 x$ .

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

Cancel the common factors.

Factor $3$ out of $3$ .

$y \leq \frac{3 (- 3 x)}{3 (1)} + \frac{6}{3}$

Cancel the common factor.

$y \leq \frac{3 (- 3 x)}{3 \cdot 1} + \frac{6}{3}$

Rewrite the expression.

$y \leq \frac{- 3 x}{1} + \frac{6}{3}$

Divide $- 3 x$ by $1$ .

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

Divide $6$ by $3$ .

$y \leq - 3 x + 2$

Step 2

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

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

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

$m = - 3$

$b = 2$

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

Slope: $- 3$

y-intercept: $(0, 2)$

Slope: $- 3$

y-intercept: $(0, 2)$

Step 3

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- 3 x + 2$ .

$y \leq - 3 x + 2$

Step 4

Graph 9x+3y-6<=0

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