In the xy-plane, line L passes through the origin and is perpendicular to the line 4x+y=k, where k is a ?

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?

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  • PeterL
    Lv 4
    1 decade ago
    Best Answer

    slope of line 4x+y=k is -4 so slope of line L is 1/4

    Since line L passes thru origin its equation is y=x/4

    since they intersect at (t,t+1) then t+1=t/4 from line L equation.

    Hence, 3t/4=-1 and t=-4/3 ANSWER

  • 1 decade ago

    Let y=Mx be first line.

    The second line in slope-intercept format is y=k-4x. So M=1/4 (sneaky, hah).

    Now we have y=x/4 and y=k-4x. Since (t,t+1) satisfies both equations, FROM THE FIRST, t+1= t/4 and 3t= -4 or t= -4/3.

    In the second, t+1 = k - 4(t), from which k=5t+1. Find k.

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