Algebra Examples

$y > - \frac{4}{3} x - 1 y$

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

Simplify each term.

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Step 1.1.1.1

Combine $x$ and $\frac{4}{3}$ .

$y > - \frac{x \cdot 4}{3} - 1 y$

Step 1.1.1.2

Move $4$ to the left of $x$ .

$y > - \frac{4 \cdot x}{3} - 1 y$

Step 1.1.1.3

Rewrite $- 1 y$ as $- y$ .

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

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 $y$ to both sides of the inequality.

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

Step 1.1.2.2

Add $y$ and $y$ .

$2 y > - \frac{4 x}{3}$

Step 1.1.3

Divide each term in $2 y > - \frac{4 x}{3}$ by $2$ and simplify.

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Step 1.1.3.1

Divide each term in $2 y > - \frac{4 x}{3}$ by $2$ .

$\frac{2 y}{2} > \frac{- \frac{4 x}{3}}{2}$

Step 1.1.3.2

Simplify the left side.

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Step 1.1.3.2.1

Cancel the common factor of $2$ .

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Step 1.1.3.2.1.1

Cancel the common factor.

$\frac{2 y}{2} > \frac{- \frac{4 x}{3}}{2}$

Step 1.1.3.2.1.2

Divide $y$ by $1$ .

$y > \frac{- \frac{4 x}{3}}{2}$

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.

$y > - \frac{4 x}{3} \cdot \frac{1}{2}$

Step 1.1.3.3.2

Cancel the common factor of $2$ .

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Step 1.1.3.3.2.1

Move the leading negative in $- \frac{4 x}{3}$ into the numerator.

$y > \frac{- 4 x}{3} \cdot \frac{1}{2}$

Step 1.1.3.3.2.2

Factor $2$ out of $- 4 x$ .

$y > \frac{2 (- 2 x)}{3} \cdot \frac{1}{2}$

Step 1.1.3.3.2.3

Cancel the common factor.

$y > \frac{2 (- 2 x)}{3} \cdot \frac{1}{2}$

Step 1.1.3.3.2.4

Rewrite the expression.

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

Step 1.1.3.3.3

Move the negative in front of the fraction.

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

Step 1.2

Reorder terms.

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

Step 1.3

Remove parentheses.

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

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 $y = m x + b$ .

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

$b = 0$

Step 2.2

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

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

y-intercept: $(0, 0)$

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

y-intercept: $(0, 0)$

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $- \frac{2}{3} x$ .

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

Step 4