Trigonometry Examples

$- 6 x + 5 y > - 30$

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

Add $6 x$ to both sides of the inequality.

$5 y > - 30 + 6 x$

Step 1.1.2

Divide each term in $5 y > - 30 + 6 x$ by $5$ and simplify.

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Step 1.1.2.1

Divide each term in $5 y > - 30 + 6 x$ by $5$ .

$\frac{5 y}{5} > \frac{- 30}{5} + \frac{6 x}{5}$

Step 1.1.2.2

Simplify the left side.

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Step 1.1.2.2.1

Cancel the common factor of $5$ .

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Step 1.1.2.2.1.1

Cancel the common factor.

$\frac{5 y}{5} > \frac{- 30}{5} + \frac{6 x}{5}$

Step 1.1.2.2.1.2

Divide $y$ by $1$ .

$y > \frac{- 30}{5} + \frac{6 x}{5}$

Step 1.1.2.3

Simplify the right side.

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Step 1.1.2.3.1

Divide $- 30$ by $5$ .

$y > - 6 + \frac{6 x}{5}$

Step 1.2

Rearrange terms.

$y > \frac{6 x}{5} - 6$

Step 1.3

Reorder terms.

$y > \frac{6}{5} x - 6$

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 $y = m x + b$ .

$m = \frac{6}{5}$

$b = - 6$

Step 2.2

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

Slope: $\frac{6}{5}$

y-intercept: $(0, - 6)$

Slope: $\frac{6}{5}$

y-intercept: $(0, - 6)$

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $\frac{6}{5} x - 6$ .

$y > \frac{6}{5} x - 6$

Step 4