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!!!!!
- nozar nazariLv 71 decade agoFavorite Answer
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 =
God bless you.
- railbuffLv 71 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
The lines intersect at (-3/2, -1/2)
t = -3/2 and t+1 = -1/2Source(s): Retired math teacher
- galjourLv 44 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
- NorthstarLv 71 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
y - x = (t + 1) - t = 1
y - x = k/17 - 4k/17 = -3k/17
-3k/17 = 1
-3k = 17
k = -17/3