SOLUTION: Are the following lines parallel, perpendicular, or neither? L1 with equation x – 2y = 10 L2 with equation 2x + y = 2 A) Perpendicular B) Neither C) Parallel

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Are the following lines parallel, perpendicular, or neither? L1 with equation x – 2y = 10 L2 with equation 2x + y = 2 A) Perpendicular B) Neither C) Parallel       Log On


   

Question 90636: Are the following lines parallel, perpendicular, or neither? L1 with equation x – 2y = 10 L2 with equation 2x + y = 2

A) Perpendicular B) Neither C) Parallel
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Convert x – 2y = 10 into slope intercept form
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-2y=10 Start with the given equation


1x-2y-1x=10-1x Subtract 1x from both sides


-2y=-1x%2B10 Simplify


%28-2y%29%2F%28-2%29=%28-1x%2B10%29%2F%28-2%29 Divide both sides by -2 to isolate y


y+=+%28-1x%29%2F%28-2%29%2B%2810%29%2F%28-2%29 Break up the fraction on the right hand side


y+=+%281%2F2%29x-5 Reduce and simplify


The original equation 1x-2y=10 (standard form) is equivalent to y+=+%281%2F2%29x-5 (slope-intercept form)


The equation y+=+%281%2F2%29x-5 is in the form y=mx%2Bb where m=1%2F2 is the slope and b=-5 is the y intercept.






Convert 2x + y = 2 into slope intercept form
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)


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


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


1y=-2x%2B2 Simplify


The original equation 2x%2B1y=2 (standard form) is equivalent to y+=+-2x%2B2 (slope-intercept form)


The equation y+=+-2x%2B2 is in the form y=mx%2Bb where m=-2 is the slope and b=2 is the y intercept.





Now multiply the two slopes we found earlier:
%281%2F2%29%28-2%29=-2%2F2=-1

Since the product of the two slopes is -1, this means they are perpendicular