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# What is the value of k in the function?

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What is the value of k in the function f(x) = 2-k / 5x+k if the graph of the function passes through the point (-1, 1/2)?

Thank you.

May 6, 2022

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What is the value of k in the function f(x)?

Hello Julia!

$$f(x) = 2-k / 5\cdot x+k\\ so\\ f(x)=-\frac{k}{5}x+k+2$$

$$-\frac{k}{5}x= -\frac{k}{5}x(x+1)+\frac{k}{5}$$

$$f(x)= -\frac{k}{5}x(x+1)+\frac{k}{5}+k+2\\\color{blue} f(x)= -\frac{k}{5}x(x+1)+\frac{6}{5}k+2$$

$$\frac{6}{5}k+2=\frac{1}{2}\\ \frac{6}{5}k=-\frac{3}{2}\\ k=-\frac{3\cdot 5}{2\cdot 6}\\ \color{blue}k=-\frac{5}{4}$$

$$f(x)=2+\frac{5}{4\cdot 5}\cdot(-1)-\frac{5}{4}\\ {\color{blue}\frac{1}{2}}=2+\frac{5}{4\cdot 5}\cdot ({\color{blue}-1})-\frac{5}{4}\color{blue}$$

y                          x

!

May 6, 2022
edited by asinus  May 6, 2022