Algebra Examples

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

Step 1

Find the slope and y-intercept of the first equation.

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Step 1.1

Rewrite in slope-intercept form.

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Step 1.1.1

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 1.1.2

Simplify the right side.

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Step 1.1.2.1

Simplify each term.

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Step 1.1.2.1.1

Combine $x$ and $\frac{3}{4}$ .

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

Step 1.1.2.1.2

Move $3$ to the left of $x$ .

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

Step 1.1.3

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

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Step 1.1.3.1

Reorder terms.

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

Step 1.1.3.2

Remove parentheses.

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

Step 1.2

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m_{1} = - \frac{3}{4}$

$b = 2$

$m_{1} = - \frac{3}{4}$

$b = 2$

Step 2

Find the slope and y-intercept of the second equation.

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Step 2.1

Rewrite in slope-intercept form.

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Step 2.1.1

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 2.1.2

Subtract $3 x$ from both sides of the equation.

$- 4 y = - 8 - 3 x$

Step 2.1.3

Divide each term in $- 4 y = - 8 - 3 x$ by $- 4$ and simplify.

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Step 2.1.3.1

Divide each term in $- 4 y = - 8 - 3 x$ by $- 4$ .

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

Step 2.1.3.2

Simplify the left side.

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Step 2.1.3.2.1

Cancel the common factor of $- 4$ .

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Step 2.1.3.2.1.1

Cancel the common factor.

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

Step 2.1.3.2.1.2

Divide $y$ by $1$ .

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

Step 2.1.3.3

Simplify the right side.

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Step 2.1.3.3.1

Simplify each term.

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Step 2.1.3.3.1.1

Divide $- 8$ by $- 4$ .

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

Step 2.1.3.3.1.2

Dividing two negative values results in a positive value.

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

Step 2.1.4

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

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Step 2.1.4.1

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

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

Step 2.1.4.2

Reorder terms.

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

Step 2.2

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m_{2} = \frac{3}{4}$

$b = 2$

$m_{2} = \frac{3}{4}$

$b = 2$

Step 3

Compare the slopes $m$ of the two equations.

$m_{1} = - \frac{3}{4}, m_{2} = \frac{3}{4}$

Step 4

Compare the two slopes in the decimal form. If the slopes are equal, then the lines are parallel. If the slopes are not equal, then the lines are not parallel.

$m_{1} = - 0.75, m_{2} = 0.75$

Step 5

The equations are not parallel because the slopes of the two lines are not equal.

Not Parallel

Step 6