Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

full question below: In the xy-plane, line L passes through the origin and is perpendicular to the line 4x+y=k

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), that is the value of t?

I tried a long time to figure this out. It is from a textbook so I don't think there is a problem with the question.

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  • 1 decade ago
    Best Answer

    First off, we need the slope of the line L.

    Since L is perpendicular to 4x+y=k, we find the latter's slope: m = -B/A (since the equation's in the form Ax + By = C).

    m = -B/A = -4/1 = -4

    L's slope should be the negative reciprocal of m: 1/4.

    We know it's y-intercept is 0, since it goes through the origin (0,0).

    So L's slope-intercept equation is y = (1/4)·x +0, or simply y = (1/4)·x

    To solve for t, we put the point (t,t+1) into either equation. But since the second equation (4x + y = k) introduces another unneeded variable, use the one we found for L:

    y = (1/4)·x

    Substitute:

    t+1 = (1/4)·t

    t = -1 + t/4

    (3/4)·t = -1

    t = -4/3

    t+1 = -1/3

    Source(s): Me, a math teacher.
  • 1 decade ago

    First rewrite the perpendicular line in slope intercept form:

    y = -4x + k

    So the line L's slope must be the negative reciprocal of -4 and since it passes thru the origin it's y-intercept (b) = 0

    So the equation of line L is y = (1/4)x

    To find t, plug (t, t+1) in to the equation y = (1/4)x

    t+1 = (1/4)t

    1 = (-3/4)t

    -4/3 = t

  • 1 decade ago

    First, it's perpendicular to 4x+y=k. That means its slope is the negative reciprocal of 4x+y=k. I'll figure that out first.

    4x+y=k

    y=-4x+k

    Slope is -4

    Slope of desired line is +1/4

    My desired line looks like this:

    y=1/4x +b

    My line passes through (0,0)

    Therefore 0=(1/4)0+b, b=0

    My desired line is y=1/4x

    The slope of my line between(t,t+1) and (0,0) is 1/4

    Therefore [(t+1)-0]/[t-0] = 1/4

    (t+1)/t=1/4

    4t+4=t

    3t = -4

    t = -4/3

    The value of t is -4/3

    Verification: y=1/4x

    (-1/3) = 1/4(-4/3)

    -1/3 = -1/3

    Thank you for an extremely interesting problem. If I knew how to give you stars or 10 points from this stupid computer, I would!

  • 1 decade ago

    The original line is y = -4x+k, so has slope -4. That means L has slope 1/4. Two points on L are (0,0) and (t,t+1), so they must give the same slope: (t+1-0)/(t-0)=1/4. Now just solve for t.

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  • 3 years ago

    enable y=Mx be first line. the 2nd line in slope-intercept format is y=ok-4x. So M=one million/4 (sneaky, hah). we've now y=x/4 and y=ok-4x. on account that (t,t+one million) satisfies the two equations, FROM the 1st, t+one million= t/4 and 3t= -4 or t= -4/3. interior the 2nd, t+one million = ok - 4(t), from which ok=5t+one million. discover ok.

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