In the xy-plane, line l passes through the origin and is perpendicular to the line 3x + 2y = k. k is constant.If the 2 lines intersect at (t, t + 1), what is t? Im confused for the fact that I dont know the value of k.
You don't actually need k:
You can rewrite this as:
2y=-3x+k , or:
y = -1.5 x + (k/2)
The slope of this line is -1.5 (or -3/2)
Line l is perpendicular to this line, which means it has slope +2/3 (the negative reciprocal of -3/2)
Line l passes through the origin, so it has y-intercept of 0
So, line l has equation:
y = (2/3)x + 0
y = (2/3)x
If the two lines intersect at (t,t+1), then l has to go through the point (t,t+1). That means, we can plug in x=t and y=t+1, and the equation should be true. So:
multiplying both sides by 3:
3t+3 = 2t
You could, from here, if you wanted, use all of this information to figure out k, since you now know that the first line must pass through the point (-3,-2). But you don't actually need k to figure out t.
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