<p>In the xy-plane, line l passes through the origin and is perpendicular to the line 4x+y=k, where k is constant. If the two lines intersect at the point (t, t+1), what is the value of t?</p>
<p>A) -4/3
B) -5/4
C) 3/4
D) 5/4
E) 4/3</p>
<p>the answer is A but don't get why, thanks in advance =]</p>
<p>bump…anyone?</p>
<p>4x + y = k
y = -4x + k
slope of this line given is -4
slope of the line perpendicular to it, or line L, is 1/4, or 0.25</p>
<p>passes through origin, so the constant, or the number you add, is 0
so…
the equation for line L is</p>
<p>y = (1/4)x + 0</p>
<p>or simply</p>
<p>y = 0.25x</p>
<p>plug (t, t+1) into this equation, where t is x, and t+1 is y, to solve for t
you don’t use the other line (y = -4x + k) because for this given point, although BOTH equations work (since they intersect at this common point), the other one has an extra variable in the way (k)</p>
<p>t+1 = (0.25)(t)
0.75t = -1
(3/4)t = -1
t= -4/3</p>
<p>basically in general you find the equation of a line with x and y and a point if they are not already given, and you plug the point into the equation. if there’s 2 lines, use the one with only the variables x and y. if there’s 2 points, use the one with the variable you solve for (t)</p>
<p>if you have any other questions, post them here</p>