Pre-Algebra Examples

$- \frac{1}{2} x - 4 y + 2 = 0$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

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 1.2

Simplify the left side.

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Step 1.2.1

Combine $x$ and $\frac{1}{2}$ .

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

Step 1.3

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

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Step 1.3.1

Add $\frac{x}{2}$ to both sides of the equation.

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

Step 1.3.2

Subtract $2$ from both sides of the equation.

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

Step 1.4

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

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Step 1.4.1

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

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

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Cancel the common factor of $- 4$ .

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Step 1.4.2.1.1

Cancel the common factor.

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

Step 1.4.2.1.2

Divide $y$ by $1$ .

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

Step 1.4.3

Simplify the right side.

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Step 1.4.3.1

Simplify each term.

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Step 1.4.3.1.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 1.4.3.1.2

Move the negative in front of the fraction.

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

Step 1.4.3.1.3

Multiply $\frac{x}{2} (- \frac{1}{4})$ .

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Step 1.4.3.1.3.1

Multiply $\frac{x}{2}$ by $\frac{1}{4}$ .

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

Step 1.4.3.1.3.2

Multiply $2$ by $4$ .

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

Step 1.4.3.1.4

Cancel the common factor of $- 2$ and $- 4$ .

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Step 1.4.3.1.4.1

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

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

Step 1.4.3.1.4.2

Cancel the common factors.

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Step 1.4.3.1.4.2.1

Factor $- 2$ out of $- 4$ .

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

Step 1.4.3.1.4.2.2

Cancel the common factor.

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

Step 1.4.3.1.4.2.3

Rewrite the expression.

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

Step 1.5

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

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Step 1.5.1

Reorder terms.

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

Step 1.5.2

Remove parentheses.

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

Step 2

Using the slope-intercept form, the y-intercept is $\frac{1}{2}$ .

$b = \frac{1}{2}$

Step 3

y-intercept in point form.

$(0, \frac{1}{2})$

Step 4