SOLUTION: Determine which two equations represent perpendicular lines a. y=6x-7 b. y=1/6x+7 c. y=-1/6x+7 d. y=1/6x-7 Show all work

Algebra ->  Equations -> SOLUTION: Determine which two equations represent perpendicular lines a. y=6x-7 b. y=1/6x+7 c. y=-1/6x+7 d. y=1/6x-7 Show all work      Log On


   

Question 117110: Determine which two equations represent perpendicular lines
a. y=6x-7
b. y=1/6x+7
c. y=-1/6x+7
d. y=1/6x-7
Show all work
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

by definition, the lines through the points are perpendicular if their slopes are negative reciprocals.
a. y=6x-7..........this line has slope 6
b. y=1%2F6x%2B7...........this line has slope 1%2F6
c. y=-1%2F6x%2B7...........this line has slope -1%2F6
d. y=1%2F6x-7...........this line has slope 1%2F6
since only -1%2F6 is negative reciprocal of 6, lines a and c are perpendicular.

Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


6x%2By=7

-0166666666666667x%2By=-7





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


6x%2By=7 Start with the given equation



1y=7-6x Subtract 6+x from both sides



1y=-6x%2B7 Rearrange the equation



y=%28-6x%2B7%29%2F%281%29 Divide both sides by 1



y=%28-6%2F1%29x%2B%287%29%2F%281%29 Break up the fraction



y=-6x%2B7 Reduce



Now lets graph y=-6x%2B7 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-6x%2B7%29+ Graph of y=-6x%2B7




So let's solve for y on the second equation


-0166666666666667x%2By=-7 Start with the given equation



1y=-7%2B0166666666666667x Add 0166666666666667+x to both sides



1y=%2B0166666666666667x-7 Rearrange the equation



y=%28%2B0166666666666667x-7%29%2F%281%29 Divide both sides by 1



y=%28%2B0166666666666667%2F1%29x%2B%28-7%29%2F%281%29 Break up the fraction



y=166666666666667x-7 Reduce





Now lets add the graph of y=166666666666667x-7 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-6x%2B7%2C166666666666667x-7%29+ Graph of y=-6x%2B7(red) and y=166666666666667x-7(green)


From the graph, we can see that the two lines intersect at the point (14%2F166666666666673,1.16666666666663e%2B15%2F166666666666673) (note: you might have to adjust the window to see the intersection)