SOLUTION: Determine whether the lines are parallel,perpendicular,neither,unknown or impossible to say.7x+2y=14;7y=2x-5

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Determine whether the lines are parallel,perpendicular,neither,unknown or impossible to say.7x+2y=14;7y=2x-5       Log On


   

Question 580809: Determine whether the lines are parallel,perpendicular,neither,unknown or impossible to say.7x+2y=14;7y=2x-5
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
We have to look at the slopes, if they exist.
Subtracting 7x from both sides of the equal sign in 7x%2B2y=14, and then dividing both sides by 2, we get to the slope-intercept form of the equation:
7x%2B2y=14 --> 2y=-7x%2B14 --> y=%28-7%2F2%29x%2B2
The slope is -7%2F2, the coefficient of the x.
It's even easier for the other equation. Just divide both sides by 7.
7y=2x-5 --> y=%282%2F7%29x-5%2F7
The slope is 2%2F7.
The lines these equations represent would be parallel if and only if the slopes were the same. So these lines are not parallel.
The lines would be perpendicular if the product of the slopes were -1. Let's multiply:
%28-7%2F2%29%282%2F7%29=-7%2A2%2F%282%2A7%29=-1 The lines are highlight+%28perpendicular%29.
If the slopes were different, and the product was something other than -1, the lines would be neither. Once we find the slopes, unknown is not an option.
Horizontal lines, with equations equivalent to y=somenumber, have slope=0.
The only lines that have no slope are vertical lines, whose equations are equivalent to x=somenumber. Vertical lines are parallel to other vertical lines, and perpendicular to horizontal lines. Vertical lines are neither parallel nor perpendicular to lines with non-zero slope.