Algebra Examples

$\frac{7 x - 4 y}{4} = x + 2$

Step 1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2

Rewrite in slope-intercept form.

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Step 2.1

Multiply both sides by $4$ .

$\frac{7 x - 4 y}{4} \cdot 4 = (x + 2) \cdot 4$

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 $4$ .

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Step 2.2.1.1.1

Cancel the common factor.

$\frac{7 x - 4 y}{4} \cdot 4 = (x + 2) \cdot 4$

Step 2.2.1.1.2

Rewrite the expression.

$7 x - 4 y = (x + 2) \cdot 4$

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

Simplify $(x + 2) \cdot 4$ .

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Step 2.2.2.1.1

Apply the distributive property.

$7 x - 4 y = x \cdot 4 + 2 \cdot 4$

Step 2.2.2.1.2

Simplify the expression.

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Step 2.2.2.1.2.1

Move $4$ to the left of $x$ .

$7 x - 4 y = 4 \cdot x + 2 \cdot 4$

Step 2.2.2.1.2.2

Multiply $2$ by $4$ .

$7 x - 4 y = 4 x + 8$

Step 2.3

Solve for $y$ .

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Step 2.3.1

Move all terms not containing $y$ to the right side of the equation.

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Step 2.3.1.1

Subtract $7 x$ from both sides of the equation.

$- 4 y = 4 x + 8 - 7 x$

Step 2.3.1.2

Subtract $7 x$ from $4 x$ .

$- 4 y = - 3 x + 8$

Step 2.3.2

Divide each term in $- 4 y = - 3 x + 8$ by $- 4$ and simplify.

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Step 2.3.2.1

Divide each term in $- 4 y = - 3 x + 8$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 3 x}{- 4} + \frac{8}{- 4}$

Step 2.3.2.2

Simplify the left side.

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Step 2.3.2.2.1

Cancel the common factor of $- 4$ .

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Step 2.3.2.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- 3 x}{- 4} + \frac{8}{- 4}$

Step 2.3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 3 x}{- 4} + \frac{8}{- 4}$

Step 2.3.2.3

Simplify the right side.

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Step 2.3.2.3.1

Simplify each term.

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Step 2.3.2.3.1.1

Dividing two negative values results in a positive value.

$y = \frac{3 x}{4} + \frac{8}{- 4}$

Step 2.3.2.3.1.2

Divide $8$ by $- 4$ .

$y = \frac{3 x}{4} - 2$

Step 2.4

Reorder terms.

$y = \frac{3}{4} x - 2$