Examples

y = 3 x

$y = 3 x$ ,

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

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

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

$y = m x + b$ , where

m

$m$ is the slope and

b

$b$ is the y-intercept.

y = m x + b

$y = m x + b$

Step 1.2

Find the values of

m

$m$ and

b

$b$ using the form

y = m x + b

$y = m x + b$ .

m_{1} = 3

$m_{1} = 3$

b = 0

$b = 0$

m_{1} = 3

$m_{1} = 3$

b = 0

$b = 0$

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

$y = m x + b$ , where

m

$m$ is the slope and

b

$b$ is the y-intercept.

y = m x + b

$y = m x + b$

Step 2.1.2

Simplify the right side.

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Step 2.1.2.1

Combine

x

$x$ and

\frac{1}{3}

$\frac{1}{3}$ .

y = - \frac{x}{3}

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

y = - \frac{x}{3}

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

Step 2.1.3

Write in

y = m x + b

$y = m x + b$ form.

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Step 2.1.3.1

Reorder terms.

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

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

Step 2.1.3.2

Remove parentheses.

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

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

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

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

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

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

Step 2.2

Find the values of

m

$m$ and

b

$b$ using the form

y = m x + b

$y = m x + b$ .

m_{2} = - \frac{1}{3}

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

b = 0

$b = 0$

m_{2} = - \frac{1}{3}

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

b = 0

$b = 0$

Step 3

Compare the slopes

m

$m$ of the two equations.

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

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

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} = 3, m_{2} = - 0. ¯ 3

$m_{1} = 3, m_{2} = - 0.\overline{3}$

Step 5

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

Not Parallel

Step 6

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