Determine if Parallel y=3x+5 , y=-1/3x+5

$y = 3 x + 5$ , $y = - \frac{1}{3} x + 5$

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

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

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

$m_{1} = 3$

$b = 5$

$m_{1} = 3$

$b = 5$

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

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Simplify the right side.

Combine $x$ and $\frac{1}{3}$ .

$y = - \frac{x}{3} + 5$

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

Reorder terms.

$y = - (\frac{1}{3} x) + 5$

Remove parentheses.

$y = - \frac{1}{3} x + 5$

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

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

$b = 5$

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

$b = 5$

Compare the slopes $m$ of the two equations.

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

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.

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

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

Not Parallel

Determine if Parallel y=3x+5 , y=-1/3x+5

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