Algebra Examples

$x \leq - 4 y - 8$

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

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

$- 4 y - 8 \geq x$

Step 1.1.2

Add $8$ to both sides of the inequality.

$- 4 y \geq x + 8$

Step 1.1.3

Divide each term in $- 4 y \geq x + 8$ by $- 4$ and simplify.

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Step 1.1.3.1

Divide each term in $- 4 y \geq x + 8$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 y}{- 4} \leq \frac{x}{- 4} + \frac{8}{- 4}$

Step 1.1.3.2

Simplify the left side.

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Step 1.1.3.2.1

Cancel the common factor of $- 4$ .

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Step 1.1.3.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} \leq \frac{x}{- 4} + \frac{8}{- 4}$

Step 1.1.3.2.1.2

Divide $y$ by $1$ .

$y \leq \frac{x}{- 4} + \frac{8}{- 4}$

Step 1.1.3.3

Simplify the right side.

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Step 1.1.3.3.1

Simplify each term.

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Step 1.1.3.3.1.1

Move the negative in front of the fraction.

$y \leq - \frac{x}{4} + \frac{8}{- 4}$

Step 1.1.3.3.1.2

Divide $8$ by $- 4$ .

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

Step 1.2

Reorder terms.

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

Step 1.3

Remove parentheses.

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

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 $y = m x + b$ .

$m = - \frac{1}{4}$

$b = - 2$

Step 2.2

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

Slope: $- \frac{1}{4}$

y-intercept: $(0, - 2)$

Slope: $- \frac{1}{4}$

y-intercept: $(0, - 2)$

Step 3

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

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

Step 4