math

In the xy-plane, line l passes through the origin and is perpendicular to the line 4x+y=k, where k is a constant. If the two lines intersect at the point (t,t+1), what is the value of t?
I tried drawing a picture of the problem described above, but I don't understand what I need to do to solve it.

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  1. y = m x + b
    y = -4 x + k
    slope, m = -4
    so
    slope of perpendicular = -1/-4 = .25
    so form of line two is
    y = .25 x + b but b = 0 because through (0,0)
    then
    both go through (t, t+1)
    line 1
    t+1 = -4 t + k so 5 t = k-1
    line 2
    t+1 = .25 t so .75 t = - 1
    t = -1/.75 = - 1 1/3

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  2. Thank you for your help. I have one question. How did you get .75 from t+1?

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