Trigonometry Examples

$3 x + 5 y = 15$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

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 1.2

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

$5 y = 15 - 3 x$

Step 1.3

Divide each term in $5 y = 15 - 3 x$ by $5$ and simplify.

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Step 1.3.1

Divide each term in $5 y = 15 - 3 x$ by $5$ .

$\frac{5 y}{5} = \frac{15}{5} + \frac{- 3 x}{5}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $5$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{15}{5} + \frac{- 3 x}{5}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{15}{5} + \frac{- 3 x}{5}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Divide $15$ by $5$ .

$y = 3 + \frac{- 3 x}{5}$

Step 1.3.3.1.2

Move the negative in front of the fraction.

$y = 3 - \frac{3 x}{5}$

Step 1.4

Write in $y = m x + b$ form.

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Step 1.4.1

Reorder $3$ and $- \frac{3 x}{5}$ .

$y = - \frac{3 x}{5} + 3$

Step 1.4.2

Reorder terms.

$y = - (\frac{3}{5} x) + 3$

Step 1.4.3

Remove parentheses.

$y = - \frac{3}{5} x + 3$

Step 2

Using the slope-intercept form, the slope is $- \frac{3}{5}$ .

$m = - \frac{3}{5}$

Step 3

The equation of a perpendicular line to $y = - \frac{3}{5} x + 3$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{- \frac{3}{5}}$

Step 4

Simplify the result.

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Step 4.1

Cancel the common factor of $1$ and $- 1$ .

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Step 4.1.1

Rewrite $1$ as $- 1 (- 1)$ .

$m_{perpendicular} = - \frac{- 1 \cdot - 1}{- \frac{3}{5}}$

Step 4.1.2

Move the negative in front of the fraction.

$m_{perpendicular} = \frac{1}{\frac{3}{5}}$

Step 4.2

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = 1 (\frac{5}{3})$

Step 4.3

Multiply $\frac{5}{3}$ by $1$ .

$m_{perpendicular} = \frac{5}{3}$

Step 4.4

Multiply $- - \frac{5}{3}$ .

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Step 4.4.1

Multiply $- 1$ by $- 1$ .

$m_{perpendicular} = 1 (\frac{5}{3})$

Step 4.4.2

Multiply $\frac{5}{3}$ by $1$ .

$m_{perpendicular} = \frac{5}{3}$

Step 5