Pre-Algebra Examples

$- 3 x - 2 y \geq 6$

Step 1

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

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Step 1.1

Solve for $y$ .

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Step 1.1.1

Add $3 x$ to both sides of the inequality.

$- 2 y \geq 6 + 3 x$

Step 1.1.2

Divide each term in $- 2 y \geq 6 + 3 x$ by $- 2$ and simplify.

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Step 1.1.2.1

Divide each term in $- 2 y \geq 6 + 3 x$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 y}{- 2} \leq \frac{6}{- 2} + \frac{3 x}{- 2}$

Step 1.1.2.2

Simplify the left side.

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Step 1.1.2.2.1

Cancel the common factor of $- 2$ .

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Step 1.1.2.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} \leq \frac{6}{- 2} + \frac{3 x}{- 2}$

Step 1.1.2.2.1.2

Divide $y$ by $1$ .

$y \leq \frac{6}{- 2} + \frac{3 x}{- 2}$

Step 1.1.2.3

Simplify the right side.

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Step 1.1.2.3.1

Simplify each term.

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Step 1.1.2.3.1.1

Divide $6$ by $- 2$ .

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

Step 1.1.2.3.1.2

Move the negative in front of the fraction.

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

Step 1.2

Rearrange terms.

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

Step 1.3

Reorder terms.

$y \leq - (\frac{3}{2} x) - 3$

Step 1.4

Remove parentheses.

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

Step 2

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

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Step 2.1

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

$m = - \frac{3}{2}$

$b = - 3$

Step 2.2

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

Slope: $- \frac{3}{2}$

y-intercept: $(0, - 3)$

Slope: $- \frac{3}{2}$

y-intercept: $(0, - 3)$

Step 3

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

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

Step 4