Which graph is the solution?

Algebra Level 2

Which graph among the given ones is a solution to my equation? 1 2 y + 1 2 y = 1 2 x \frac{1}{2^y} + \frac{1}{2^y} = \frac{1}{2^x}

E A C D B

Hana Wehbi by Hana Wehbi , 51, USA

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2 solutions

Chew-Seong Cheong
Feb 14, 2018

1 2 y + 1 2 y = 1 2 x 2 2 y = 1 2 x 2 1 − y = 2 − x 1 − y = − x ⟹ y = x + 1 \begin{aligned} \frac 1{2^y} + \frac 1{2^y} & = \frac 1{2^x} \\ \frac 2{2^y} & = \frac 1{2^x} \\ 2^{1-y} & = 2^{-x} \\ 1-y & = - x \\ \implies y & = x + 1 \end{aligned}

Therefore, graph E \boxed{\text{E}} is the solution.

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Thank you and I wrote it correct this time :)

Hana Wehbi - 3 years, 3 months ago
Blan Morrison
Feb 14, 2018

First, we simplify the fractions into negative exponents: 2 − y + 2 − y = 2 − x 2^{-y}+2^{-y}=2^{-x} ⟹ 2 − y + 1 = 2 − x \implies~2^{-y+1}=2^{-x} ⟹ − y + 1 = − x \implies~-y+1=-x ⟹ y = x + 1 \implies~y=x+1 The fifth graph, E, has a slope of 1 and a y-intercept of 1, just like the equation.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Thank you for sharing your solution.

Hana Wehbi - 3 years, 3 months ago

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