Trigonometry Examples

$2 x - 5 y > 6$

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 $2 x$ from both sides of the inequality.

$- 5 y > 6 - 2 x$

Step 1.1.2

Divide each term in $- 5 y > 6 - 2 x$ by $- 5$ and simplify.

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Step 1.1.2.1

Divide each term in $- 5 y > 6 - 2 x$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 y}{- 5} < \frac{6}{- 5} + \frac{- 2 x}{- 5}$

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.

$\frac{- 5 y}{- 5} < \frac{6}{- 5} + \frac{- 2 x}{- 5}$

Step 1.1.2.2.1.2

Divide $y$ by $1$ .

$y < \frac{6}{- 5} + \frac{- 2 x}{- 5}$

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

Move the negative in front of the fraction.

$y < - \frac{6}{5} + \frac{- 2 x}{- 5}$

Step 1.1.2.3.1.2

Dividing two negative values results in a positive value.

$y < - \frac{6}{5} + \frac{2 x}{5}$

Step 1.2

Rearrange terms.

$y < \frac{2 x}{5} - \frac{6}{5}$

Step 1.3

Reorder terms.

$y < \frac{2}{5} x - \frac{6}{5}$

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 $y = m x + b$ .

$m = \frac{2}{5}$

$b = - \frac{6}{5}$

Step 2.2

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

Slope: $\frac{2}{5}$

y-intercept: $(0, - \frac{6}{5})$

Slope: $\frac{2}{5}$

y-intercept: $(0, - \frac{6}{5})$

Step 3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $\frac{2}{5} x - \frac{6}{5}$ .

$y < \frac{2}{5} x - \frac{6}{5}$

Step 4