Graph -12x-2y>=-42

$- 12 x - 2 y \geq - 42$

Step 1

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

Solve for $y$ .

Add $12 x$ to both sides of the inequality.

$- 2 y \geq - 42 + 12 x$

Divide each term in $- 2 y \geq - 42 + 12 x$ by $- 2$ and simplify.

Divide each term in $- 2 y \geq - 42 + 12 x$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 y}{- 2} \leq \frac{- 42}{- 2} + \frac{12 x}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} \leq \frac{- 42}{- 2} + \frac{12 x}{- 2}$

Divide $y$ by $1$ .

$y \leq \frac{- 42}{- 2} + \frac{12 x}{- 2}$

Simplify the right side.

Simplify each term.

Divide $- 42$ by $- 2$ .

$y \leq 21 + \frac{12 x}{- 2}$

Cancel the common factor of $12$ and $- 2$ .

Factor $2$ out of $12 x$ .

$y \leq 21 + \frac{2 (6 x)}{- 2}$

Move the negative one from the denominator of $\frac{6 x}{- 1}$ .

$y \leq 21 - 1 \cdot (6 x)$

Rewrite $- 1 \cdot (6 x)$ as $- (6 x)$ .

$y \leq 21 - (6 x)$

Multiply $6$ by $- 1$ .

$y \leq 21 - 6 x$

Rearrange terms.

$y \leq - 6 x + 21$

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 $y = m x + b$ .

$m = - 6$

$b = 21$

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

Slope: $- 6$

y-intercept: $(0, 21)$

Slope: $- 6$

y-intercept: $(0, 21)$

Step 3

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- 6 x + 21$ .

$y \leq - 6 x + 21$

Step 4

Graph -12x-2y>=-42

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