Trigonometry Examples

$\frac{x}{4} - \frac{3 y}{5} = 8$

Step 1

Solve the equation for $y$ .

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Step 1.1

Subtract $\frac{x}{4}$ from both sides of the equation.

$- \frac{3 y}{5} = 8 - \frac{x}{4}$

Step 1.2

Multiply both sides of the equation by $- \frac{5}{3}$ .

$- \frac{5}{3} (- \frac{3 y}{5}) = - \frac{5}{3} (8 - \frac{x}{4})$

Step 1.3

Simplify both sides of the equation.

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Step 1.3.1

Simplify the left side.

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Step 1.3.1.1

Simplify $- \frac{5}{3} (- \frac{3 y}{5})$ .

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Step 1.3.1.1.1

Cancel the common factor of $5$ .

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Step 1.3.1.1.1.1

Move the leading negative in $- \frac{5}{3}$ into the numerator.

$\frac{- 5}{3} (- \frac{3 y}{5}) = - \frac{5}{3} (8 - \frac{x}{4})$

Step 1.3.1.1.1.2

Move the leading negative in $- \frac{3 y}{5}$ into the numerator.

$\frac{- 5}{3} \cdot \frac{- 3 y}{5} = - \frac{5}{3} (8 - \frac{x}{4})$

Step 1.3.1.1.1.3

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{3} \cdot \frac{- 3 y}{5} = - \frac{5}{3} (8 - \frac{x}{4})$

Step 1.3.1.1.1.4

Cancel the common factor.

$\frac{5 \cdot - 1}{3} \cdot \frac{- 3 y}{5} = - \frac{5}{3} (8 - \frac{x}{4})$

Step 1.3.1.1.1.5

Rewrite the expression.

$\frac{- 1}{3} (- 3 y) = - \frac{5}{3} (8 - \frac{x}{4})$

Step 1.3.1.1.2

Cancel the common factor of $3$ .

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Step 1.3.1.1.2.1

Factor $3$ out of $- 3 y$ .

$\frac{- 1}{3} (3 (- y)) = - \frac{5}{3} (8 - \frac{x}{4})$

Step 1.3.1.1.2.2

Cancel the common factor.

$\frac{- 1}{3} (3 (- y)) = - \frac{5}{3} (8 - \frac{x}{4})$

Step 1.3.1.1.2.3

Rewrite the expression.

$- - y = - \frac{5}{3} (8 - \frac{x}{4})$

Step 1.3.1.1.3

Multiply.

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Step 1.3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{5}{3} (8 - \frac{x}{4})$

Step 1.3.1.1.3.2

Multiply $y$ by $1$ .

$y = - \frac{5}{3} (8 - \frac{x}{4})$

Step 1.3.2

Simplify the right side.

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Step 1.3.2.1

Simplify $- \frac{5}{3} (8 - \frac{x}{4})$ .

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Step 1.3.2.1.1

Apply the distributive property.

$y = - \frac{5}{3} \cdot 8 - \frac{5}{3} (- \frac{x}{4})$

Step 1.3.2.1.2

Multiply $- \frac{5}{3} \cdot 8$ .

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Step 1.3.2.1.2.1

Multiply $8$ by $- 1$ .

$y = - 8 (\frac{5}{3}) - \frac{5}{3} (- \frac{x}{4})$

Step 1.3.2.1.2.2

Combine $- 8$ and $\frac{5}{3}$ .

$y = \frac{- 8 \cdot 5}{3} - \frac{5}{3} (- \frac{x}{4})$

Step 1.3.2.1.2.3

Multiply $- 8$ by $5$ .

$y = \frac{- 40}{3} - \frac{5}{3} (- \frac{x}{4})$

Step 1.3.2.1.3

Multiply $- \frac{5}{3} (- \frac{x}{4})$ .

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Step 1.3.2.1.3.1

Multiply $- 1$ by $- 1$ .

$y = \frac{- 40}{3} + 1 (\frac{5}{3}) \frac{x}{4}$

Step 1.3.2.1.3.2

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

$y = \frac{- 40}{3} + \frac{5}{3} \cdot \frac{x}{4}$

Step 1.3.2.1.3.3

Multiply $\frac{5}{3}$ by $\frac{x}{4}$ .

$y = \frac{- 40}{3} + \frac{5 x}{3 \cdot 4}$

Step 1.3.2.1.3.4

Multiply $3$ by $4$ .

$y = \frac{- 40}{3} + \frac{5 x}{12}$

Step 1.3.2.1.4

Move the negative in front of the fraction.

$y = - \frac{40}{3} + \frac{5 x}{12}$

Step 1.4

Reorder $- \frac{40}{3}$ and $\frac{5 x}{12}$ .

$y = \frac{5 x}{12} - \frac{40}{3}$

Step 2

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be $0$ or $1$ for each of its variables. In this case, the degree of variable $y$ is $1$ and the degree of variable $x$ is $1$ .

Linear