Algebra Examples

$8 x + y \geq - 5$ $x + 5 y < 2$

Step 1

Graph $8 x + y \geq - 5$ .

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Step 1.1

Write in $y = m x + b$ form.

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Step 1.1.1

Subtract $8 x$ from both sides of the inequality.

$y \geq - 5 - 8 x$

Step 1.1.2

Rearrange terms.

$y \geq - 8 x - 5$

Step 1.2

Use the slope-intercept form to find the slope and y-intercept.

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Step 1.2.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.2.2

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = - 8$

$b = - 5$

Step 1.2.3

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

Slope: $- 8$

y-intercept: $(0, - 5)$

Slope: $- 8$

y-intercept: $(0, - 5)$

Step 1.3

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $- 8 x - 5$ .

$y \geq - 8 x - 5$

Step 2

Graph $x + 5 y < 2$ .

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Step 2.1

Write in $y = m x + b$ form.

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Step 2.1.1

Solve for $y$ .

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Step 2.1.1.1

Subtract $x$ from both sides of the inequality.

$5 y < 2 - x$

Step 2.1.1.2

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

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Step 2.1.1.2.1

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

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

Step 2.1.1.2.2

Simplify the left side.

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Step 2.1.1.2.2.1

Cancel the common factor of $5$ .

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Step 2.1.1.2.2.1.1

Cancel the common factor.

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

Step 2.1.1.2.2.1.2

Divide $y$ by $1$ .

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

Step 2.1.1.2.3

Simplify the right side.

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Step 2.1.1.2.3.1

Move the negative in front of the fraction.

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

Step 2.1.2

Rearrange terms.

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

Step 2.1.3

Reorder terms.

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

Step 2.1.4

Remove parentheses.

$y < - \frac{1}{5} x + \frac{2}{5}$

Step 2.2

Use the slope-intercept form to find the slope and y-intercept.

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Step 2.2.1

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = - \frac{1}{5}$

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

Step 2.2.2

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

Slope: $- \frac{1}{5}$

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

Slope: $- \frac{1}{5}$

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

Step 2.3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- \frac{1}{5} x + \frac{2}{5}$ .

$y < - \frac{1}{5} x + \frac{2}{5}$

Step 3

Plot each graph on the same coordinate system.

$8 x + y \geq - 5$

$x + 5 y < 2$

Step 4