Pre-Algebra Examples

$y - (- 1) = \frac{4}{13} x - (- 1)$

Step 1

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

Step 2

Multiply both sides by $13$ .

$13 (y - (- 1)) = 13 (\frac{4}{13} x - (- 1))$

Step 3

Simplify the left side.

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Step 3.1

Simplify $13 (y - (- 1))$ .

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Step 3.1.1

Multiply $- 1$ by $- 1$ .

$13 (y + 1) = 13 (\frac{4}{13} x - (- 1))$

Step 3.1.2

Apply the distributive property.

$13 y + 13 \cdot 1 = 13 (\frac{4}{13} x - (- 1))$

Step 3.1.3

Multiply $13$ by $1$ .

$13 y + 13 = 13 (\frac{4}{13} x - (- 1))$

Step 4

Simplify the right side.

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Step 4.1

Simplify $13 (\frac{4}{13} x - (- 1))$ .

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Step 4.1.1

Simplify each term.

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Step 4.1.1.1

Combine $\frac{4}{13}$ and $x$ .

$13 y + 13 = 13 (\frac{4 x}{13} - (- 1))$

Step 4.1.1.2

Multiply $- 1$ by $- 1$ .

$13 y + 13 = 13 (\frac{4 x}{13} + 1)$

Step 4.1.2

Simplify terms.

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Step 4.1.2.1

Apply the distributive property.

$13 y + 13 = 13 \frac{4 x}{13} + 13 \cdot 1$

Step 4.1.2.2

Cancel the common factor of $13$ .

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Step 4.1.2.2.1

Cancel the common factor.

$13 y + 13 = 13 \frac{4 x}{13} + 13 \cdot 1$

Step 4.1.2.2.2

Rewrite the expression.

$13 y + 13 = 4 x + 13 \cdot 1$

Step 4.1.2.3

Multiply $13$ by $1$ .

$13 y + 13 = 4 x + 13$

Step 5

Rewrite the equation.

$4 x + 13 = 13 y + 13$

Step 6

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

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Step 6.1

Subtract $13 y$ from both sides of the equation.

$4 x + 13 - 13 y = 13$

Step 6.2

Move $13$ .

$4 x - 13 y + 13 = 13$

Step 7

Move all terms not containing a variable to the right side of the equation.

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Step 7.1

Subtract $13$ from both sides of the equation.

$4 x - 13 y = 13 - 13$

Step 7.2

Subtract $13$ from $13$ .

$4 x - 13 y = 0$

Step 8