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
    Best 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 =

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

    God bless you.

  • 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
  • 3 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

  • 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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