Pre-Algebra Examples

$y = - \frac{2}{5} x - 1$

Step 1

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

Step 2

Multiply both sides by $5$ .

$5 y = 5 (- \frac{2}{5} x - 1)$

Step 3

Simplify the right side.

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Step 3.1

Simplify $5 (- \frac{2}{5} x - 1)$ .

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Step 3.1.1

Simplify each term.

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Step 3.1.1.1

Combine $x$ and $\frac{2}{5}$ .

$5 y = 5 (- \frac{x \cdot 2}{5} - 1)$

Step 3.1.1.2

Move $2$ to the left of $x$ .

$5 y = 5 (- \frac{2 x}{5} - 1)$

Step 3.1.2

Simplify terms.

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Step 3.1.2.1

Apply the distributive property.

$5 y = 5 (- \frac{2 x}{5}) + 5 \cdot - 1$

Step 3.1.2.2

Cancel the common factor of $5$ .

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Step 3.1.2.2.1

Move the leading negative in $- \frac{2 x}{5}$ into the numerator.

$5 y = 5 \frac{- 2 x}{5} + 5 \cdot - 1$

Step 3.1.2.2.2

Cancel the common factor.

$5 y = 5 \frac{- 2 x}{5} + 5 \cdot - 1$

Step 3.1.2.2.3

Rewrite the expression.

$5 y = - 2 x + 5 \cdot - 1$

Step 3.1.2.3

Multiply $5$ by $- 1$ .

$5 y = - 2 x - 5$

Step 4

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

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Step 4.1

Add $2 x$ to both sides of the equation.

$5 y + 2 x = - 5$

Step 4.2

Reorder $5 y$ and $2 x$ .

$2 x + 5 y = - 5$

Step 5