Graph -4y<=2/3x-2

$- 4 y \leq \frac{2}{3} x - 2$

Step 1

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

Divide each term in $- 4 y \leq \frac{2}{3} x - 2$ by $- 4$ and simplify.

Divide each term in $- 4 y \leq \frac{2}{3} x - 2$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 y}{- 4} \geq \frac{\frac{2}{3} x}{- 4} + \frac{- 2}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} \geq \frac{\frac{2}{3} x}{- 4} + \frac{- 2}{- 4}$

Divide $y$ by $1$ .

$y \geq \frac{\frac{2}{3} x}{- 4} + \frac{- 2}{- 4}$

Simplify the right side.

Simplify each term.

Combine $\frac{2}{3}$ and $x$ .

$y \geq \frac{\frac{2 x}{3}}{- 4} + \frac{- 2}{- 4}$

Multiply the numerator by the reciprocal of the denominator.

$y \geq \frac{2 x}{3} \cdot \frac{1}{- 4} + \frac{- 2}{- 4}$

Cancel the common factor of $2$ .

Factor $2$ out of $2 x$ .

$y \geq \frac{2 (x)}{3} \cdot \frac{1}{- 4} + \frac{- 2}{- 4}$

Factor $2$ out of $- 4$ .

$y \geq \frac{2 (x)}{3} \cdot \frac{1}{2 (- 2)} + \frac{- 2}{- 4}$

Cancel the common factor.

$y \geq \frac{2 x}{3} \cdot \frac{1}{2 \cdot - 2} + \frac{- 2}{- 4}$

Rewrite the expression.

$y \geq \frac{x}{3} \cdot \frac{1}{- 2} + \frac{- 2}{- 4}$

Multiply $\frac{x}{3}$ by $\frac{1}{- 2}$ .

$y \geq \frac{x}{3 \cdot - 2} + \frac{- 2}{- 4}$

Multiply $3$ by $- 2$ .

$y \geq \frac{x}{- 6} + \frac{- 2}{- 4}$

Move the negative in front of the fraction.

$y \geq - \frac{x}{6} + \frac{- 2}{- 4}$

Cancel the common factor of $- 2$ and $- 4$ .

Factor $- 2$ out of $- 2$ .

$y \geq - \frac{x}{6} + \frac{- 2 (1)}{- 4}$

Cancel the common factors.

Factor $- 2$ out of $- 4$ .

$y \geq - \frac{x}{6} + \frac{- 2 \cdot 1}{- 2 \cdot 2}$

Cancel the common factor.

$y \geq - \frac{x}{6} + \frac{- 2 \cdot 1}{- 2 \cdot 2}$

Rewrite the expression.

$y \geq - \frac{x}{6} + \frac{1}{2}$

Reorder terms.

$y \geq - (\frac{1}{6} x) + \frac{1}{2}$

Remove parentheses.

$y \geq - \frac{1}{6} x + \frac{1}{2}$

Step 2

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

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

$m = - \frac{1}{6}$

$b = \frac{1}{2}$

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

Slope: $- \frac{1}{6}$

y-intercept: $(0, \frac{1}{2})$

Slope: $- \frac{1}{6}$

y-intercept: $(0, \frac{1}{2})$

Step 3

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $- \frac{1}{6} x + \frac{1}{2}$ .

$y \geq - \frac{1}{6} x + \frac{1}{2}$

Step 4

Graph -4y<=2/3x-2

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