Algebra Examples

$y = - \frac{1}{3} x - 9$

Step 1

The standard form of a linear equation is $A x + B y = C$ .

Step 2

Multiply both sides by $3$ .

$3 y = 3 (- \frac{1}{3} x - 9)$

Step 3

Simplify the right side.

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Step 3.1

Simplify $3 (- \frac{1}{3} x - 9)$ .

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Step 3.1.1

Combine $x$ and $\frac{1}{3}$ .

$3 y = 3 (- \frac{x}{3} - 9)$

Step 3.1.2

Apply the distributive property.

$3 y = 3 (- \frac{x}{3}) + 3 \cdot - 9$

Step 3.1.3

Cancel the common factor of $3$ .

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Step 3.1.3.1

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

$3 y = 3 \frac{- x}{3} + 3 \cdot - 9$

Step 3.1.3.2

Cancel the common factor.

$3 y = 3 \frac{- x}{3} + 3 \cdot - 9$

Step 3.1.3.3

Rewrite the expression.

$3 y = - x + 3 \cdot - 9$

Step 3.1.4

Multiply $3$ by $- 9$ .

$3 y = - x - 27$

Step 4

Move all terms containing variables to the left side of the equation.

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Step 4.1

Add $x$ to both sides of the equation.

$3 y + x = - 27$

Step 4.2

Reorder $3 y$ and $x$ .

$x + 3 y = - 27$

Step 5