Question

Describe how to determine if two lines are parallel, perpendicular or neither. Give an example of a parallel line, a perpendicular line and a line which is neither parallel nor perpendicular to y=2/5x+7.

Answer 1

Answer:

In order to determine if two lines are parallel, perpendicular, or neither, look at their slopes. If the lines have the same slope, they are parallel. If the slopes are opposite reciprocals, then they are perpendicular. If the slopes of the lines are not any of those, then they are neither.

Parallel line: $y = \frac{2}{5} x$

Perpendicular line: $y = -\frac{5}{2} x$  

Neither: $y = 3x$

Step-by-step explanation:

In order to determine if two lines are parallel, perpendicular, or neither, look at their slopes. If the slopes of the two lines are the same, then they are parallel. If the slopes of the two lines are opposite reciprocals, then they are perpendicular. If the slopes of the lines are not any of those, then they are neither.  

The equation $y = \frac{2}{5} x+7$ is in slope-intercept form. The y is isolated and it's in $y = mx + b$ format. Whenever an equation is in slope-intercept form, the $m$, or the coefficient of the x-term, represents the slope. So, the slope of the given line is $\frac{2}{5}$. Therefore, use the rules listed previously to find lines that are parallel and perpendicular.

Parallel lines have the same slope, so an example of a parallel line would be $y = \frac{2}{5} x$.

Lines that are perpendicular have slopes that are opposite reciprocals, so an example of a perpendicular line would be $y = -\frac{5}{2} x$.

Lines that are neither do not fall into either of those categories, so an example of a line that is neither would be  $y = 3x$.