Pre-Algebra Examples

$4 x < - 16 y$

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.

$- 16 y > 4 x$

Step 1.1.2

Divide each term in $- 16 y > 4 x$ by $- 16$ and simplify.

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Step 1.1.2.1

Divide each term in $- 16 y > 4 x$ by $- 16$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 16 y}{- 16} < \frac{4 x}{- 16}$

Step 1.1.2.2

Simplify the left side.

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Step 1.1.2.2.1

Cancel the common factor of $- 16$ .

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Step 1.1.2.2.1.1

Cancel the common factor.

$\frac{- 16 y}{- 16} < \frac{4 x}{- 16}$

Step 1.1.2.2.1.2

Divide $y$ by $1$ .

$y < \frac{4 x}{- 16}$

Step 1.1.2.3

Simplify the right side.

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Step 1.1.2.3.1

Cancel the common factor of $4$ and $- 16$ .

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Step 1.1.2.3.1.1

Factor $4$ out of $4 x$ .

$y < \frac{4 (x)}{- 16}$

Step 1.1.2.3.1.2

Cancel the common factors.

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Step 1.1.2.3.1.2.1

Factor $4$ out of $- 16$ .

$y < \frac{4 x}{4 \cdot - 4}$

Step 1.1.2.3.1.2.2

Cancel the common factor.

$y < \frac{4 x}{4 \cdot - 4}$

Step 1.1.2.3.1.2.3

Rewrite the expression.

$y < \frac{x}{- 4}$

Step 1.1.2.3.2

Move the negative in front of the fraction.

$y < - \frac{x}{4}$

Step 1.2

Reorder terms.

$y < - (\frac{1}{4} x)$

Step 1.3

Remove parentheses.

$y < - \frac{1}{4} x$

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 $y = m x + b$ .

$m = - \frac{1}{4}$

$b = 0$

Step 2.2

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

Slope: $- \frac{1}{4}$

y-intercept: $(0, 0)$

Slope: $- \frac{1}{4}$

y-intercept: $(0, 0)$

Step 3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- \frac{1}{4} x$ .

$y < - \frac{1}{4} x$

Step 4