SOLUTION: Are the following lines parallel, perpendicular, or neither? L1 with equation x – 6y = 12 L2 with equation 6x + y = 6

Algebra ->  Points-lines-and-rays -> SOLUTION: Are the following lines parallel, perpendicular, or neither? L1 with equation x – 6y = 12 L2 with equation 6x + y = 6       Log On


   

Question 111293: Are the following lines parallel, perpendicular, or neither?
L1 with equation x – 6y = 12
L2 with equation 6x + y = 6
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First find the slope of x – 6y = 12

Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)
Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)


1x-6y=12 Start with the given equation


1x-6y-1x=12-1x Subtract 1x from both sides


-6y=-1x%2B12 Simplify


%28-6y%29%2F%28-6%29=%28-1x%2B12%29%2F%28-6%29 Divide both sides by -6 to isolate y


y+=+%28-1x%29%2F%28-6%29%2B%2812%29%2F%28-6%29 Break up the fraction on the right hand side


y+=+%281%2F6%29x-2 Reduce and simplify


The original equation 1x-6y=12 (standard form) is equivalent to y+=+%281%2F6%29x-2 (slope-intercept form)


The equation y+=+%281%2F6%29x-2 is in the form y=mx%2Bb where m=1%2F6 is the slope and b=-2 is the y intercept.





Now find the slope of 6x + y = 6

Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)
Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)


6x%2B1y=6 Start with the given equation


6x%2B1y-6x=6-6x Subtract 6x from both sides


1y=-6x%2B6 Simplify


The original equation 6x%2B1y=6 (standard form) is equivalent to y+=+-6x%2B6 (slope-intercept form)


The equation y+=+-6x%2B6 is in the form y=mx%2Bb where m=-6 is the slope and b=6 is the y intercept.






Since their product is %281%2F6%29%28-6%29=-6%2F6=-1 this means the two lines are perpendicular