Algebra Examples

$x + 2 y \geq - 5$

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

Subtract $x$ from both sides of the inequality.

$2 y \geq - 5 - x$

Step 1.1.2

Divide each term in $2 y \geq - 5 - x$ by $2$ and simplify.

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Step 1.1.2.1

Divide each term in $2 y \geq - 5 - x$ by $2$ .

$\frac{2 y}{2} \geq \frac{- 5}{2} + \frac{- x}{2}$

Step 1.1.2.2

Simplify the left side.

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Step 1.1.2.2.1

Cancel the common factor of $2$ .

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Step 1.1.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} \geq \frac{- 5}{2} + \frac{- x}{2}$

Step 1.1.2.2.1.2

Divide $y$ by $1$ .

$y \geq \frac{- 5}{2} + \frac{- x}{2}$

Step 1.1.2.3

Simplify the right side.

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Step 1.1.2.3.1

Simplify each term.

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Step 1.1.2.3.1.1

Move the negative in front of the fraction.

$y \geq - \frac{5}{2} + \frac{- x}{2}$

Step 1.1.2.3.1.2

Move the negative in front of the fraction.

$y \geq - \frac{5}{2} - \frac{x}{2}$

Step 1.2

Rearrange terms.

$y \geq - \frac{x}{2} - \frac{5}{2}$

Step 1.3

Reorder terms.

$y \geq - (\frac{1}{2} x) - \frac{5}{2}$

Step 1.4

Remove parentheses.

$y \geq - \frac{1}{2} x - \frac{5}{2}$

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 $y = m x + b$ .

$m = - \frac{1}{2}$

$b = - \frac{5}{2}$

Step 2.2

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

Slope: $- \frac{1}{2}$

y-intercept: $(0, - \frac{5}{2})$

Slope: $- \frac{1}{2}$

y-intercept: $(0, - \frac{5}{2})$

Step 3

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $- \frac{1}{2} x - \frac{5}{2}$ .

$y \geq - \frac{1}{2} x - \frac{5}{2}$

Step 4