Algebra Examples

Are the lines defined by the equations $y + 5 x = 1$ and $y = 5 x + 4$ parallel?

Step 1

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

Tap for more steps...

Step 1.1

Rewrite in slope-intercept form.

Tap for more steps...

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 $5 x$ from both sides of the equation.

$y = 1 - 5 x$

Step 1.1.3

Reorder $1$ and $- 5 x$ .

$y = - 5 x + 1$

Step 1.2

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

$m_{1} = - 5$

$b = 1$

$m_{1} = - 5$

$b = 1$

Step 2

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

Tap for more steps...

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 $y = m x + b$ .

$m_{2} = 5$

$b = 4$

$m_{2} = 5$

$b = 4$

Step 3

Compare the slopes $m$ of the two equations.

$m_{1} = - 5, m_{2} = 5$

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.

$m_{1} = - 5, m_{2} = 5$

Step 5

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

Not Parallel

Step 6