Algebra Examples

$\frac{x}{2} + \frac{y}{6} = 1$

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

Subtract $\frac{x}{2}$ from both sides of the equation.

$\frac{y}{6} = 1 - \frac{x}{2}$

Step 2.2

Multiply both sides of the equation by $6$ .

$6 \frac{y}{6} = 6 (1 - \frac{x}{2})$

Step 2.3

Simplify both sides of the equation.

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Step 2.3.1

Simplify the left side.

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Step 2.3.1.1

Cancel the common factor of $6$ .

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Step 2.3.1.1.1

Cancel the common factor.

$6 \frac{y}{6} = 6 (1 - \frac{x}{2})$

Step 2.3.1.1.2

Rewrite the expression.

$y = 6 (1 - \frac{x}{2})$

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

Simplify $6 (1 - \frac{x}{2})$ .

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Step 2.3.2.1.1

Apply the distributive property.

$y = 6 \cdot 1 + 6 (- \frac{x}{2})$

Step 2.3.2.1.2

Multiply $6$ by $1$ .

$y = 6 + 6 (- \frac{x}{2})$

Step 2.3.2.1.3

Cancel the common factor of $2$ .

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Step 2.3.2.1.3.1

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

$y = 6 + 6 \frac{- x}{2}$

Step 2.3.2.1.3.2

Factor $2$ out of $6$ .

$y = 6 + 2 (3) \frac{- x}{2}$

Step 2.3.2.1.3.3

Cancel the common factor.

$y = 6 + 2 \cdot 3 \frac{- x}{2}$

Step 2.3.2.1.3.4

Rewrite the expression.

$y = 6 + 3 (- x)$

Step 2.3.2.1.4

Multiply $- 1$ by $3$ .

$y = 6 - 3 x$

Step 2.4

Reorder $6$ and $- 3 x$ .

$y = - 3 x + 6$