Pre-Algebra Examples

$- 4 x - 3 y > 12$

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 $4 x$ to both sides of the inequality.

$- 3 y > 12 + 4 x$

Step 1.1.2

Divide each term in $- 3 y > 12 + 4 x$ by $- 3$ and simplify.

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Step 1.1.2.1

Divide each term in $- 3 y > 12 + 4 x$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 y}{- 3} < \frac{12}{- 3} + \frac{4 x}{- 3}$

Step 1.1.2.2

Simplify the left side.

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Step 1.1.2.2.1

Cancel the common factor of $- 3$ .

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Step 1.1.2.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} < \frac{12}{- 3} + \frac{4 x}{- 3}$

Step 1.1.2.2.1.2

Divide $y$ by $1$ .

$y < \frac{12}{- 3} + \frac{4 x}{- 3}$

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 $12$ by $- 3$ .

$y < - 4 + \frac{4 x}{- 3}$

Step 1.1.2.3.1.2

Move the negative in front of the fraction.

$y < - 4 - \frac{4 x}{3}$

Step 1.2

Rearrange terms.

$y < - \frac{4 x}{3} - 4$

Step 1.3

Reorder terms.

$y < - (\frac{4}{3} x) - 4$

Step 1.4

Remove parentheses.

$y < - \frac{4}{3} x - 4$

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 $y = m x + b$ .

$m = - \frac{4}{3}$

$b = - 4$

Step 2.2

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

Slope: $- \frac{4}{3}$

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

Slope: $- \frac{4}{3}$

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

Step 3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- \frac{4}{3} x - 4$ .

$y < - \frac{4}{3} x - 4$

Step 4