Algebra Examples

$\frac{2}{3} x + 4 (y - 2) = 0$

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

Simplify the left side.

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Combine $\frac{2}{3}$ and $x$ .

$\frac{2 x}{3} + 4 (y - 2) = 0$

Step 2.1.1.2

Apply the distributive property.

$\frac{2 x}{3} + 4 y + 4 \cdot - 2 = 0$

Step 2.1.1.3

Multiply $4$ by $- 2$ .

$\frac{2 x}{3} + 4 y - 8 = 0$

Step 2.2

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

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Step 2.2.1

Subtract $\frac{2 x}{3}$ from both sides of the equation.

$4 y - 8 = - \frac{2 x}{3}$

Step 2.2.2

Add $8$ to both sides of the equation.

$4 y = - \frac{2 x}{3} + 8$

Step 2.3

Divide each term in $4 y = - \frac{2 x}{3} + 8$ by $4$ and simplify.

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Step 2.3.1

Divide each term in $4 y = - \frac{2 x}{3} + 8$ by $4$ .

$\frac{4 y}{4} = \frac{- \frac{2 x}{3}}{4} + \frac{8}{4}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $4$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{- \frac{2 x}{3}}{4} + \frac{8}{4}$

Step 2.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- \frac{2 x}{3}}{4} + \frac{8}{4}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Simplify each term.

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Step 2.3.3.1.1

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{2 x}{3} \cdot \frac{1}{4} + \frac{8}{4}$

Step 2.3.3.1.2

Cancel the common factor of $2$ .

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Step 2.3.3.1.2.1

Move the leading negative in $- \frac{2 x}{3}$ into the numerator.

$y = \frac{- 2 x}{3} \cdot \frac{1}{4} + \frac{8}{4}$

Step 2.3.3.1.2.2

Factor $2$ out of $- 2 x$ .

$y = \frac{2 (- x)}{3} \cdot \frac{1}{4} + \frac{8}{4}$

Step 2.3.3.1.2.3

Factor $2$ out of $4$ .

$y = \frac{2 (- x)}{3} \cdot \frac{1}{2 (2)} + \frac{8}{4}$

Step 2.3.3.1.2.4

Cancel the common factor.

$y = \frac{2 (- x)}{3} \cdot \frac{1}{2 \cdot 2} + \frac{8}{4}$

Step 2.3.3.1.2.5

Rewrite the expression.

$y = \frac{- x}{3} \cdot \frac{1}{2} + \frac{8}{4}$

Step 2.3.3.1.3

Multiply $\frac{- x}{3}$ by $\frac{1}{2}$ .

$y = \frac{- x}{3 \cdot 2} + \frac{8}{4}$

Step 2.3.3.1.4

Multiply $3$ by $2$ .

$y = \frac{- x}{6} + \frac{8}{4}$

Step 2.3.3.1.5

Move the negative in front of the fraction.

$y = - \frac{x}{6} + \frac{8}{4}$

Step 2.3.3.1.6

Divide $8$ by $4$ .

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

Step 2.4

Write in $y = m x + b$ form.

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Step 2.4.1

Reorder terms.

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

Step 2.4.2

Remove parentheses.

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