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?

Question

I tried drawing a picture of the problem described above, but I don't understand what I need to do to solve it.

Answer 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

Answer 2

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