+2499 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 ?
+130547 A line passing through the origin and perpendicular to the line 4x + y = k will have a slope of (1/4) and the equation of this line will be y = (1/4)x
And at (t, t +1 ) we have that
t + 1 = (1/4)t
(3/4) t = -1
t = -4/3 then t + 1 will = -1/3
And we can find k as
4t +[ t + 1 ] = k
-16/3 - 1/3 = k = -17/3
Here's a graph of both lines and the intersection point :.......https://www.desmos.com/calculator/c5qsf7jlo2
+130547 A line passing through the origin and perpendicular to the line 4x + y = k will have a slope of (1/4) and the equation of this line will be y = (1/4)x
And at (t, t +1 ) we have that
t + 1 = (1/4)t
(3/4) t = -1
t = -4/3 then t + 1 will = -1/3
And we can find k as
4t +[ t + 1 ] = k
-16/3 - 1/3 = k = -17/3
Here's a graph of both lines and the intersection point :.......https://www.desmos.com/calculator/c5qsf7jlo2
