Algebra Examples

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

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 $\frac{1}{2}$ .

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

Step 1.3

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

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

Step 1.4

Divide each term in $- y = \frac{3}{4} + \frac{x}{2}$ by $- 1$ and simplify.

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Step 1.4.1

Divide each term in $- y = \frac{3}{4} + \frac{x}{2}$ by $- 1$ .

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

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Dividing two negative values results in a positive value.

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

Step 1.4.2.2

Divide $y$ by $1$ .

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

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

Move the negative one from the denominator of $\frac{\frac{3}{4}}{- 1}$ .

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

Step 1.4.3.1.2

Rewrite $- 1 \cdot \frac{3}{4}$ as $- \frac{3}{4}$ .

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

Step 1.4.3.1.3

Move the negative one from the denominator of $\frac{\frac{x}{2}}{- 1}$ .

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

Step 1.4.3.1.4

Rewrite $- 1 \cdot \frac{x}{2}$ as $- \frac{x}{2}$ .

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

Step 1.5

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

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Step 1.5.1

Reorder $- \frac{3}{4}$ and $- \frac{x}{2}$ .

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

Step 1.5.2

Reorder terms.

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

Step 1.5.3

Remove parentheses.

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

Step 2

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

$m = - \frac{1}{2}$

Step 3