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In the xy-plane, a triangle T is formed by x-axis, y-axis, and the li

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In the xy-plane, a triangle T is formed by x-axis, y-axis, and the li [#permalink]

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In the xy-plane, a triangle T is formed by x-axis, y-axis, and the line with equation y=4x+k. If the area of the triangle T is smaller than 2, what is the range of k?

A. k<-4, 4<k
B. -4<k<4
C. k<-3, 5<k
D. -3<k<5
E. k<-2, 8<k
[Reveal] Spoiler: OA

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Re: In the xy-plane, a triangle T is formed by x-axis, y-axis, and the li [#permalink]

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area of triangle = 1/2*(k)*(k/4)<2 => k^2 < 16 => (k+4)(k-4)<0 => -4<k<4 ->option B
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Re: In the xy-plane, a triangle T is formed by x-axis, y-axis, and the li [#permalink]

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==>Since y=4x+k passes through (0,k) and (-k/4,0), from the area of the triangle=(1/2)k(k/4)<2, you get k2<16, k2-16<0, (k-4)(k+4)<0, -4<k<4.

The answer is B.
Answer: B
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Re: In the xy-plane, a triangle T is formed by x-axis, y-axis, and the li   [#permalink] 07 May 2017, 17:03
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