Algebra Examples

$8 x - 2 y = 4$ and $x + 4 y = - 12$

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

Subtract $8 x$ from both sides of the equation.

$- 2 y = 4 - 8 x$

Step 1.1.3

Divide each term in $- 2 y = 4 - 8 x$ by $- 2$ and simplify.

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Step 1.1.3.1

Divide each term in $- 2 y = 4 - 8 x$ by $- 2$ .

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

Step 1.1.3.2

Simplify the left side.

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Step 1.1.3.2.1

Cancel the common factor of $- 2$ .

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Step 1.1.3.2.1.1

Cancel the common factor.

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

Step 1.1.3.2.1.2

Divide $y$ by $1$ .

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

Step 1.1.3.3

Simplify the right side.

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Step 1.1.3.3.1

Simplify each term.

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Step 1.1.3.3.1.1

Divide $4$ by $- 2$ .

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

Step 1.1.3.3.1.2

Cancel the common factor of $- 8$ and $- 2$ .

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Step 1.1.3.3.1.2.1

Factor $- 2$ out of $- 8 x$ .

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

Step 1.1.3.3.1.2.2

Cancel the common factors.

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Step 1.1.3.3.1.2.2.1

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

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

Step 1.1.3.3.1.2.2.2

Cancel the common factor.

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

Step 1.1.3.3.1.2.2.3

Rewrite the expression.

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

Step 1.1.3.3.1.2.2.4

Divide $4 x$ by $1$ .

$y = - 2 + 4 x$

Step 1.1.4

Reorder $- 2$ and $4 x$ .

$y = 4 x - 2$

Step 1.2

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

$m_{1} = 4$

$b = - 2$

$m_{1} = 4$

$b = - 2$

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 $x$ from both sides of the equation.

$4 y = - 12 - x$

Step 2.1.3

Divide each term in $4 y = - 12 - x$ by $4$ and simplify.

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Step 2.1.3.1

Divide each term in $4 y = - 12 - x$ by $4$ .

$\frac{4 y}{4} = \frac{- 12}{4} + \frac{- x}{4}$

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.

$\frac{4 y}{4} = \frac{- 12}{4} + \frac{- x}{4}$

Step 2.1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 12}{4} + \frac{- x}{4}$

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 $- 12$ by $4$ .

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

Step 2.1.3.3.1.2

Move the negative in front of the fraction.

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

Step 2.1.4

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

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Step 2.1.4.1

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

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

Step 2.1.4.2

Reorder terms.

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

Step 2.1.4.3

Remove parentheses.

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

Step 2.2

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

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

$b = - 3$

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

$b = - 3$

Step 3

Compare the slopes $m$ of the two equations.

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

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.

$m_{1} = 4, m_{2} = - 0.25$

Step 5

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

Not Parallel

Step 6