SOLUTION: Please help, i dont understand this! Are the following lines parallel, perpendicular, or neither? L1 with equation x – 6y = 24 L2 with equation 6x + y = 6

Algebra ->  Systems-of-equations -> SOLUTION: Please help, i dont understand this! Are the following lines parallel, perpendicular, or neither? L1 with equation x – 6y = 24 L2 with equation 6x + y = 6       Log On


   

Question 113465: Please help, i dont understand this!
Are the following lines parallel, perpendicular, or neither?
L1 with equation x – 6y = 24
L2 with equation 6x + y = 6
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Parallel lines have slopes that are equal, and perpendicular lines have slopes that are the negative reciprocal of each other m%5B1%5D=%28-1%29%2Fm%5B2%5D.

Now the problem is to find the slope on each of the two lines and compare them. The equations are currently in standard form, so we need to convert them to slope-intercept form. The slope-intercept form is y=mx%2Bb where m is the slope. All that needs to be done is rearrange the equations so they have y on the left and everything else on the right.

x-6y=24
-6y=-x%2B24 Add -x to both sides
y=%281%2F6%29x-4 Divide both sides by -6

Now we know the slope of the first line is m%5B1%5D=1%2F6

Let's do the second one the same way.

6x%2By=6
y=-6x%2B6 A -6x to both sides
Now we know the slope of the second line is m%5B2%5D=-6

Comparing them we see that m%5B1%5D=-%281%2Fm%5B2%5D%29, therefore the lines are perpendicular.

Hope this helps,
John