Graph x-4<=-2(y+6)

$x - 4 \leq - 2 (y + 6)$

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

Solve for $y$ .

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

$- 2 (y + 6) \geq x - 4$

Divide each term in $- 2 (y + 6) \geq x - 4$ by $- 2$ and simplify.

Divide each term in $- 2 (y + 6) \geq x - 4$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $y + 6$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Divide $- 4$ by $- 2$ .

$y + 6 \leq - \frac{x}{2} + 2$

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

Subtract $6$ from both sides of the inequality.

$y \leq - \frac{x}{2} + 2 - 6$

Subtract $6$ from $2$ .

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

Reorder terms.

$y \leq - (\frac{1}{2} x) - 4$

Remove parentheses.

$y \leq - \frac{1}{2} x - 4$

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

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

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

$b = - 4$

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: $(0, - 4)$

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

y-intercept: $(0, - 4)$

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- \frac{1}{2} x - 4$ .

$y \leq - \frac{1}{2} x - 4$

Graph x-4<=-2(y+6)

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