# In the xy-plane, line l passes through the origin and is perpendicular to the line 4x+y=k, where k is a..(cont?

constant. If the two lines intersect at teh point (t, t+1), what is the value of t?

Help please? Please explain too! Thanks!!!!!

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• 1 decade ago
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eq l, y/x=1/4,y=1/4x,then t+1=(1/4)t & 4t+t+1=k

======>3/4t=-1,t=-4/3 & k must be =

= -16/3-4/3+1=-20/3+1=-17/3

God bless you.

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• 1 decade ago

The slopes of perpendicular lines are negative reciprocals

4x + y = k has slope -4

The required line has slope 1/4

and is therefore of the form

x - 4y = c, where c is a constant

The line passes through he origin, so, if x = 0 and y = 0, then c = 0

The equation of the line is x-4y = 0

If the two lines intersect at (x, x+1)

Then y = x + 1

x - 4(x + 1) = 0

x - 3x - 3 = 0

-2x = 3

x = -3/2

x+1 = -3/2 + 1

= -1/2

The lines intersect at (-3/2, -1/2)

t = -3/2 and t+1 = -1/2

Source(s): Retired math teacher
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• 4 years ago

First rewrite the perpendicular line in slope intercept form: y = -4x + ok So the line L's slope may be the adverse reciprocal of -4 and because it passes via the beginning place that is y-intercept (b) = 0 So the equation of line L is y = (a million/4)x to discover t, plug (t, t+a million) in to the equation y = (a million/4)x t+a million = (a million/4)t a million = (-3/4)t -4/3 = t

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• 1 decade ago

The equation of the two lines are:

4x + y = k

x - 4y = 0

Add four times the first equation to the second.

17x = 4k

x = 4k/17 = t

Subtract four times the second equation from the first.

17y = k

y = k/17 = t + 1

________

We have:

y - x = (t + 1) - t = 1

But

y - x = k/17 - 4k/17 = -3k/17

So

-3k/17 = 1

-3k = 17

k = -17/3

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