Trigonometry Examples

$3 x + 4 y > 16$

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

Subtract $3 x$ from both sides of the inequality.

$4 y > 16 - 3 x$

Step 1.1.2

Divide each term in $4 y > 16 - 3 x$ by $4$ and simplify.

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Step 1.1.2.1

Divide each term in $4 y > 16 - 3 x$ by $4$ .

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

Step 1.1.2.2

Simplify the left side.

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Step 1.1.2.2.1

Cancel the common factor of $4$ .

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Step 1.1.2.2.1.1

Cancel the common factor.

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

Step 1.1.2.2.1.2

Divide $y$ by $1$ .

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

Step 1.1.2.3

Simplify the right side.

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Step 1.1.2.3.1

Simplify each term.

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Step 1.1.2.3.1.1

Divide $16$ by $4$ .

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

Step 1.1.2.3.1.2

Move the negative in front of the fraction.

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

Step 1.2

Rearrange terms.

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

Step 1.3

Reorder terms.

$y > - (\frac{3}{4} x) + 4$

Step 1.4

Remove parentheses.

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

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 $y = m x + b$ .

$m = - \frac{3}{4}$

$b = 4$

Step 2.2

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

Slope: $- \frac{3}{4}$

y-intercept: $(0, 4)$

Slope: $- \frac{3}{4}$

y-intercept: $(0, 4)$

Step 3

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

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

Step 4