Algebra Examples

$\frac{x}{4} < 4 y - 3$

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.

$4 y - 3 > \frac{x}{4}$

Step 1.1.2

Add $3$ to both sides of the inequality.

$4 y > \frac{x}{4} + 3$

Step 1.1.3

Divide each term in $4 y > \frac{x}{4} + 3$ by $4$ and simplify.

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Step 1.1.3.1

Divide each term in $4 y > \frac{x}{4} + 3$ by $4$ .

$\frac{4 y}{4} > \frac{\frac{x}{4}}{4} + \frac{3}{4}$

Step 1.1.3.2

Simplify the left side.

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Step 1.1.3.2.1

Cancel the common factor of $4$ .

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Step 1.1.3.2.1.1

Cancel the common factor.

$\frac{4 y}{4} > \frac{\frac{x}{4}}{4} + \frac{3}{4}$

Step 1.1.3.2.1.2

Divide $y$ by $1$ .

$y > \frac{\frac{x}{4}}{4} + \frac{3}{4}$

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

Multiply the numerator by the reciprocal of the denominator.

$y > \frac{x}{4} \cdot \frac{1}{4} + \frac{3}{4}$

Step 1.1.3.3.1.2

Multiply $\frac{x}{4} \cdot \frac{1}{4}$ .

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Step 1.1.3.3.1.2.1

Multiply $\frac{x}{4}$ by $\frac{1}{4}$ .

$y > \frac{x}{4 \cdot 4} + \frac{3}{4}$

Step 1.1.3.3.1.2.2

Multiply $4$ by $4$ .

$y > \frac{x}{16} + \frac{3}{4}$

Step 1.2

Reorder terms.

$y > \frac{1}{16} x + \frac{3}{4}$

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 $y = m x + b$ .

$m = \frac{1}{16}$

$b = \frac{3}{4}$

Step 2.2

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

Slope: $\frac{1}{16}$

y-intercept: $(0, \frac{3}{4})$

Slope: $\frac{1}{16}$

y-intercept: $(0, \frac{3}{4})$

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $\frac{1}{16} x + \frac{3}{4}$ .

$y > \frac{1}{16} x + \frac{3}{4}$

Step 4