In the xy-plane, line l passes through the origin and is perpendicular to the line4x+y=k,?

Question

where k is a constant. If the 2 lines intersect t the point (t, t+1), what is the value of t.

Much appreciated for an explanation for the answer which is

t= -4/3

Answer 1

Find the  slope of the line

4x+y =k

y= -4x +k

m=-4

the slope of the line perpendicular to the above line will be m= -1/m

so , here, m= 1/4

and the line is passing through origin so constant k=0

so the equation of the perpendicular line (I) passing through origin is

y = (1/4)x

now the point (t, t+1) lies on this line , so replace x by t and y by (t+1) in above eqn

t+1 = (1/4)t

4t +4 = t

3t = -4

t = -4/3

Answer 2

"line l passes through the origin and is perpendicular to the line4x+y=k" mean l is "y = 4x" then replace : t = 4(t+1), then t= -4/3