Algebra Examples

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

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 $2$ .

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

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 $2$ .

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Step 2.2.1.1.1

Cancel the common factor.

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

Step 2.2.1.1.2

Rewrite the expression.

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

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

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

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Step 2.2.2.1.1

Apply the distributive property.

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

Step 2.2.2.1.2

Simplify the expression.

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Step 2.2.2.1.2.1

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

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

Step 2.2.2.1.2.2

Multiply $2$ by $2$ .

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

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.

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

Step 2.3.1.2

Subtract $7 x$ from $2 x$ .

$- 2 y = - 5 x + 4$

Step 2.3.2

Divide each term in $- 2 y = - 5 x + 4$ by $- 2$ and simplify.

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Step 2.3.2.1

Divide each term in $- 2 y = - 5 x + 4$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 5 x}{- 2} + \frac{4}{- 2}$

Step 2.3.2.2

Simplify the left side.

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Step 2.3.2.2.1

Cancel the common factor of $- 2$ .

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Step 2.3.2.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 5 x}{- 2} + \frac{4}{- 2}$

Step 2.3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 5 x}{- 2} + \frac{4}{- 2}$

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.

$y = \frac{5 x}{2} + \frac{4}{- 2}$

Step 2.3.2.3.1.2

Divide $4$ by $- 2$ .

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

Step 2.4

Reorder terms.

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