Algebra Examples

$θ = - \frac{π}{4}$

Step 1

Apply the formula $\frac{y}{x} = \tan (θ)$ .

$\frac{y}{x} = \tan (- \frac{π}{4})$

Step 2

Solve for $y$ .

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Step 2.1

Multiply both sides by $x$ .

$\frac{y}{x} x = \tan (- \frac{π}{4}) x$

Step 2.2

Simplify.

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Step 2.2.1

Simplify the left side.

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Step 2.2.1.1

Cancel the common factor of $x$ .

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Step 2.2.1.1.1

Cancel the common factor.

$\frac{y}{x} x = \tan (- \frac{π}{4}) x$

Step 2.2.1.1.2

Rewrite the expression.

$y = \tan (- \frac{π}{4}) x$

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

Simplify $\tan (- \frac{π}{4}) x$ .

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Step 2.2.2.1.1

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$y = \tan (\frac{7 π}{4}) x$

Step 2.2.2.1.2

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because tangent is negative in the fourth quadrant.

$y = - \tan (\frac{π}{4}) x$

Step 2.2.2.1.3

The exact value of $\tan (\frac{π}{4})$ is $1$ .

$y = - 1 \cdot 1 x$

Step 2.2.2.1.4

Multiply $- 1$ by $1$ .

$y = - x$