Expert: Paul Klarreich - 9/21/2008

Question
Hey paul, sorry to bother you with another math question.

(page 522)
In the xy-plane, line L passes through the origin and is perpendicular to the line 4x+y=k, where k is constant. If the two lines intersect at the point (t, t+1), what is the value of t?
a) - (4/3)
b) - (5/4)
c) 3/4
d) 5/4
e) 4/3

I know that when it says 'perpendicular' it means that when the two lines of the slope multiply it should be -1. But I don't know the slope for line l, so how do i do this problem? I really don't get this problem, so can you please kindly show the steps?

Thanks in advance!

Answer
Questioner:   Emily
Category:  Advanced Math
Private:  No
 
Subject:  Two Lines intersection
Question:  Hey paul, sorry to bother you with another math question.

(page 522)
In the xy-plane, line L passes through the origin and is perpendicular to the line 4x+y=k, where k is constant. If the two lines intersect at the point (t, t+1), what is the value of t?
a) - (4/3)
b) - (5/4)
c) 3/4
d) 5/4
e) 4/3

I know that when it says 'perpendicular' it means that when the two lines of the slope multiply it should be -1. But I don't know the slope for line l, so how do i do this problem? I really don't get this problem, so can you please kindly show the steps?

Thanks in advance!
....................................
Hi again, Emily,

A suggestion for greater success in math:  Be very careful using the vocabulary and try to write in very clear and concise English.
Instead of writing:
 
when it says 'perpendicular' it means that when the two lines of the slope multiply it should be -1.

say:

Two lines are perpendicular if the product of their slopes is -1.

Then you will know to write  m1 and m2 as the slopes and that m1 m2 = -1.

Now if L2 is the line whose equation is:  4x + y = k, solve:  y = -4x + k, then conclude that m2 = -4.

Now conclude that  m1 (-4) = -1 and that  m1 = 1/4.

Then you conclude that  L1 is   y = m1 x = 0 [passes through origin, right?]

And  L1 is  y = (1/4)x,  or  y = x/4.

Now if (t,t+1) is on the line(s), write  t + 1 = t/4  and solve the equation for t.

I'll leave that to you.