Algebra Examples

$y > - 2 x - 5 y$

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

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

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Step 1.1.1.1

Add $5 y$ to both sides of the inequality.

$y + 5 y > - 2 x$

Step 1.1.1.2

Add $y$ and $5 y$ .

$6 y > - 2 x$

Step 1.1.2

Divide each term in $6 y > - 2 x$ by $6$ and simplify.

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Step 1.1.2.1

Divide each term in $6 y > - 2 x$ by $6$ .

$\frac{6 y}{6} > \frac{- 2 x}{6}$

Step 1.1.2.2

Simplify the left side.

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Step 1.1.2.2.1

Cancel the common factor of $6$ .

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Step 1.1.2.2.1.1

Cancel the common factor.

$\frac{6 y}{6} > \frac{- 2 x}{6}$

Step 1.1.2.2.1.2

Divide $y$ by $1$ .

$y > \frac{- 2 x}{6}$

Step 1.1.2.3

Simplify the right side.

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Step 1.1.2.3.1

Cancel the common factor of $- 2$ and $6$ .

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Step 1.1.2.3.1.1

Factor $2$ out of $- 2 x$ .

$y > \frac{2 (- x)}{6}$

Step 1.1.2.3.1.2

Cancel the common factors.

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Step 1.1.2.3.1.2.1

Factor $2$ out of $6$ .

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

Step 1.1.2.3.1.2.2

Cancel the common factor.

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

Step 1.1.2.3.1.2.3

Rewrite the expression.

$y > \frac{- x}{3}$

Step 1.1.2.3.2

Move the negative in front of the fraction.

$y > - \frac{x}{3}$

Step 1.2

Reorder terms.

$y > - (\frac{1}{3} x)$

Step 1.3

Remove parentheses.

$y > - \frac{1}{3} x$

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 $y = m x + b$ .

$m = - \frac{1}{3}$

$b = 0$

Step 2.2

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

Slope: $- \frac{1}{3}$

y-intercept: $(0, 0)$

Slope: $- \frac{1}{3}$

y-intercept: $(0, 0)$

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $- \frac{1}{3} x$ .

$y > - \frac{1}{3} x$

Step 4