Pre-Algebra Examples

$y + 4 x \geq 0$ , $5 x - 4 y \leq 20$

Step 1

Graph $y + 4 x \geq 0$ .

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Step 1.1

Subtract $4 x$ from both sides of the inequality.

$y \geq - 4 x$

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 $y = m x + b$ .

$m = - 4$

$b = 0$

Step 1.2.3

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

Slope: $- 4$

y-intercept: $(0, 0)$

Slope: $- 4$

y-intercept: $(0, 0)$

Step 1.3

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $- 4 x$ .

$y \geq - 4 x$

Step 2

Graph $5 x - 4 y \leq 20$ .

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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 $5 x$ from both sides of the inequality.

$- 4 y \leq 20 - 5 x$

Step 2.1.1.2

Divide each term in $- 4 y \leq 20 - 5 x$ by $- 4$ and simplify.

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Step 2.1.1.2.1

Divide each term in $- 4 y \leq 20 - 5 x$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 y}{- 4} \geq \frac{20}{- 4} + \frac{- 5 x}{- 4}$

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 $- 4$ .

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Step 2.1.1.2.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} \geq \frac{20}{- 4} + \frac{- 5 x}{- 4}$

Step 2.1.1.2.2.1.2

Divide $y$ by $1$ .

$y \geq \frac{20}{- 4} + \frac{- 5 x}{- 4}$

Step 2.1.1.2.3

Simplify the right side.

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Step 2.1.1.2.3.1

Simplify each term.

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Step 2.1.1.2.3.1.1

Divide $20$ by $- 4$ .

$y \geq - 5 + \frac{- 5 x}{- 4}$

Step 2.1.1.2.3.1.2

Dividing two negative values results in a positive value.

$y \geq - 5 + \frac{5 x}{4}$

Step 2.1.2

Rearrange terms.

$y \geq \frac{5 x}{4} - 5$

Step 2.1.3

Reorder terms.

$y \geq \frac{5}{4} x - 5$

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 $y = m x + b$ .

$m = \frac{5}{4}$

$b = - 5$

Step 2.2.2

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

Slope: $\frac{5}{4}$

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

Slope: $\frac{5}{4}$

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

Step 2.3

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $\frac{5}{4} x - 5$ .

$y \geq \frac{5}{4} x - 5$

Step 3

Plot each graph on the same coordinate system.

$y + 4 x \geq 0$

$5 x - 4 y \leq 20$

Step 4