Precalculus Examples

$y = 8 x - 9$ , $7 y = 4 - x$

Step 1

Use the slope-intercept form to find the slope and y-intercept.

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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

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

$m_{1} = 8$

$b = - 9$

$m_{1} = 8$

$b = - 9$

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

Divide each term in $7 y = 4 - x$ by $7$ and simplify.

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Step 2.1.2.1

Divide each term in $7 y = 4 - x$ by $7$ .

$\frac{7 y}{7} = \frac{4}{7} + \frac{- x}{7}$

Step 2.1.2.2

Simplify the left side.

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Step 2.1.2.2.1

Cancel the common factor of $7$ .

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Step 2.1.2.2.1.1

Cancel the common factor.

$\frac{7 y}{7} = \frac{4}{7} + \frac{- x}{7}$

Step 2.1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{4}{7} + \frac{- x}{7}$

Step 2.1.2.3

Simplify the right side.

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Step 2.1.2.3.1

Move the negative in front of the fraction.

$y = \frac{4}{7} - \frac{x}{7}$

Step 2.1.3

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

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Step 2.1.3.1

Reorder $\frac{4}{7}$ and $- \frac{x}{7}$ .

$y = - \frac{x}{7} + \frac{4}{7}$

Step 2.1.3.2

Reorder terms.

$y = - (\frac{1}{7} x) + \frac{4}{7}$

Step 2.1.3.3

Remove parentheses.

$y = - \frac{1}{7} x + \frac{4}{7}$

Step 2.2

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

$m_{2} = - \frac{1}{7}$

$b = \frac{4}{7}$

$m_{2} = - \frac{1}{7}$

$b = \frac{4}{7}$

Step 3

Compare the slopes $m$ of the two equations.

$m_{1} = 8, m_{2} = - \frac{1}{7}$

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.

$m_{1} = 8, m_{2} = - 0.\overline{142857}$

Step 5

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

Not Parallel

Step 6