Algebra Examples

$y > - \frac{1}{2} x - 8 y$

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

Combine $x$ and $\frac{1}{2}$ .

$y > - \frac{x}{2} - 8 y$

Step 1.1.2

Move all terms containing $y$ to the left side of the inequality.

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Step 1.1.2.1

Add $8 y$ to both sides of the inequality.

$y + 8 y > - \frac{x}{2}$

Step 1.1.2.2

Add $y$ and $8 y$ .

$9 y > - \frac{x}{2}$

Step 1.1.3

Divide each term in $9 y > - \frac{x}{2}$ by $9$ and simplify.

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Step 1.1.3.1

Divide each term in $9 y > - \frac{x}{2}$ by $9$ .

$\frac{9 y}{9} > \frac{- \frac{x}{2}}{9}$

Step 1.1.3.2

Simplify the left side.

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Step 1.1.3.2.1

Cancel the common factor of $9$ .

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Step 1.1.3.2.1.1

Cancel the common factor.

$\frac{9 y}{9} > \frac{- \frac{x}{2}}{9}$

Step 1.1.3.2.1.2

Divide $y$ by $1$ .

$y > \frac{- \frac{x}{2}}{9}$

Step 1.1.3.3

Simplify the right side.

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Step 1.1.3.3.1

Multiply the numerator by the reciprocal of the denominator.

$y > - \frac{x}{2} \cdot \frac{1}{9}$

Step 1.1.3.3.2

Multiply $- \frac{x}{2} \cdot \frac{1}{9}$ .

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Step 1.1.3.3.2.1

Multiply $\frac{1}{9}$ by $\frac{x}{2}$ .

$y > - \frac{x}{9 \cdot 2}$

Step 1.1.3.3.2.2

Multiply $9$ by $2$ .

$y > - \frac{x}{18}$

Step 1.2

Reorder terms.

$y > - (\frac{1}{18} x)$

Step 1.3

Remove parentheses.

$y > - \frac{1}{18} x$

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 $y = m x + b$ .

$m = - \frac{1}{18}$

$b = 0$

Step 2.2

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

Slope: $- \frac{1}{18}$

y-intercept: $(0, 0)$

Slope: $- \frac{1}{18}$

y-intercept: $(0, 0)$

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $- \frac{1}{18} x$ .

$y > - \frac{1}{18} x$

Step 4