Algebra Examples

$- 5 x \geq 9 + 3 y$

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

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

$9 + 3 y \leq - 5 x$

Step 1.1.2

Subtract $9$ from both sides of the inequality.

$3 y \leq - 5 x - 9$

Step 1.1.3

Divide each term in $3 y \leq - 5 x - 9$ by $3$ and simplify.

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Step 1.1.3.1

Divide each term in $3 y \leq - 5 x - 9$ by $3$ .

$\frac{3 y}{3} \leq \frac{- 5 x}{3} + \frac{- 9}{3}$

Step 1.1.3.2

Simplify the left side.

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Step 1.1.3.2.1

Cancel the common factor of $3$ .

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Step 1.1.3.2.1.1

Cancel the common factor.

$\frac{3 y}{3} \leq \frac{- 5 x}{3} + \frac{- 9}{3}$

Step 1.1.3.2.1.2

Divide $y$ by $1$ .

$y \leq \frac{- 5 x}{3} + \frac{- 9}{3}$

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.

$y \leq - \frac{5 x}{3} + \frac{- 9}{3}$

Step 1.1.3.3.1.2

Divide $- 9$ by $3$ .

$y \leq - \frac{5 x}{3} - 3$

Step 1.2

Reorder terms.

$y \leq - (\frac{5}{3} x) - 3$

Step 1.3

Remove parentheses.

$y \leq - \frac{5}{3} x - 3$

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 $y = m x + b$ .

$m = - \frac{5}{3}$

$b = - 3$

Step 2.2

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

Slope: $- \frac{5}{3}$

y-intercept: $(0, - 3)$

Slope: $- \frac{5}{3}$

y-intercept: $(0, - 3)$

Step 3

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- \frac{5}{3} x - 3$ .

$y \leq - \frac{5}{3} x - 3$

Step 4