Algebra Examples

Are the lines defined by the equations $y = x + 3$ and $y = 2 x + 3$ parallel?

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 $y = m x + b$ .

$m_{1} = 1$

$b = 3$

$m_{1} = 1$

$b = 3$

Step 2

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

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Step 2.1

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 2.2

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

$m_{2} = 2$

$b = 3$

$m_{2} = 2$

$b = 3$

Step 3

Compare the slopes $m$ of the two equations.

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

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.

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

Step 5

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

Not Parallel

Step 6