Pre-Algebra Examples

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

Step 1

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

Step 2

Multiply both sides by $4$ .

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

Step 3

Simplify the left side.

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Step 3.1

Simplify $4 (y - 4)$ .

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Step 3.1.1

Apply the distributive property.

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

Step 3.1.2

Multiply $4$ by $- 4$ .

$4 y - 16 = 4 (- \frac{3}{4} \cdot (x - (- 3)))$

Step 4

Simplify the right side.

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Step 4.1

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

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Step 4.1.1

Multiply $- 1$ by $- 3$ .

$4 y - 16 = 4 (- \frac{3}{4} \cdot (x + 3))$

Step 4.1.2

Apply the distributive property.

$4 y - 16 = 4 (- \frac{3}{4} x - \frac{3}{4} \cdot 3)$

Step 4.1.3

Combine $x$ and $\frac{3}{4}$ .

$4 y - 16 = 4 (- \frac{x \cdot 3}{4} - \frac{3}{4} \cdot 3)$

Step 4.1.4

Multiply $- \frac{3}{4} \cdot 3$ .

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Step 4.1.4.1

Multiply $3$ by $- 1$ .

$4 y - 16 = 4 (- \frac{x \cdot 3}{4} - 3 (\frac{3}{4}))$

Step 4.1.4.2

Combine $- 3$ and $\frac{3}{4}$ .

$4 y - 16 = 4 (- \frac{x \cdot 3}{4} + \frac{- 3 \cdot 3}{4})$

Step 4.1.4.3

Multiply $- 3$ by $3$ .

$4 y - 16 = 4 (- \frac{x \cdot 3}{4} + \frac{- 9}{4})$

Step 4.1.5

Simplify each term.

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Step 4.1.5.1

Move $3$ to the left of $x$ .

$4 y - 16 = 4 (- \frac{3 \cdot x}{4} + \frac{- 9}{4})$

Step 4.1.5.2

Move the negative in front of the fraction.

$4 y - 16 = 4 (- \frac{3 x}{4} - \frac{9}{4})$

Step 4.1.6

Simplify terms.

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Step 4.1.6.1

Apply the distributive property.

$4 y - 16 = 4 (- \frac{3 x}{4}) + 4 (- \frac{9}{4})$

Step 4.1.6.2

Cancel the common factor of $4$ .

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Step 4.1.6.2.1

Move the leading negative in $- \frac{3 x}{4}$ into the numerator.

$4 y - 16 = 4 \frac{- 3 x}{4} + 4 (- \frac{9}{4})$

Step 4.1.6.2.2

Cancel the common factor.

$4 y - 16 = 4 \frac{- 3 x}{4} + 4 (- \frac{9}{4})$

Step 4.1.6.2.3

Rewrite the expression.

$4 y - 16 = - 3 x + 4 (- \frac{9}{4})$

Step 4.1.6.3

Cancel the common factor of $4$ .

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Step 4.1.6.3.1

Move the leading negative in $- \frac{9}{4}$ into the numerator.

$4 y - 16 = - 3 x + 4 (\frac{- 9}{4})$

Step 4.1.6.3.2

Cancel the common factor.

$4 y - 16 = - 3 x + 4 (\frac{- 9}{4})$

Step 4.1.6.3.3

Rewrite the expression.

$4 y - 16 = - 3 x - 9$

Step 5

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

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Step 5.1

Add $3 x$ to both sides of the equation.

$4 y - 16 + 3 x = - 9$

Step 5.2

Move $- 16$ .

$4 y + 3 x - 16 = - 9$

Step 5.3

Reorder $4 y$ and $3 x$ .

$3 x + 4 y - 16 = - 9$

Step 6

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

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Step 6.1

Add $16$ to both sides of the equation.

$3 x + 4 y = - 9 + 16$

Step 6.2

Add $- 9$ and $16$ .

$3 x + 4 y = 7$

Step 7