Trigonometry Examples

$\frac{1}{2} y > x + 2$

Step 1

Multiply each term in $\frac{1}{2} y > x + 2$ by $2$ to eliminate the fractions.

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Step 1.1

Multiply each term in $\frac{1}{2} y > x + 2$ by $2$ .

$\frac{1}{2} y \cdot 2 > x \cdot 2 + 2 \cdot 2$

Step 1.2

Simplify the left side.

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Step 1.2.1

Combine $\frac{1}{2}$ and $y$ .

$\frac{y}{2} \cdot 2 > x \cdot 2 + 2 \cdot 2$

Step 1.2.2

Cancel the common factor of $2$ .

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Step 1.2.2.1

Cancel the common factor.

$\frac{y}{2} \cdot 2 > x \cdot 2 + 2 \cdot 2$

Step 1.2.2.2

Rewrite the expression.

$y > x \cdot 2 + 2 \cdot 2$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Move $2$ to the left of $x$ .

$y > 2 \cdot x + 2 \cdot 2$

Step 1.3.1.2

Multiply $2$ by $2$ .

$y > 2 x + 4$

Step 2

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

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Step 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 2.2

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

$m = 2$

$b = 4$

Step 2.3

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

Slope: $2$

y-intercept: $(0, 4)$

Slope: $2$

y-intercept: $(0, 4)$

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $2 x + 4$ .

$y > 2 x + 4$

Step 4