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Biochemists studying enzyme kinetics encounter formulas of the form fox)-(K/Vx+1/V. where K and V are constants. Use this information to answer parts (a) and (b). (a) If fx) 0.2x+8, find K and V so that fx) may be written in the form fix) (K/V)x+ 1/V (b) Find the x-intercept and y-intercept of the line y (K/V)x+1/V (n terms of K and V). (a) K (Simplify your answer. Type an integer or a fraction.)

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rodolforodriguezr

Answer:

a) V=0.125 and K=0.025

b) Y-intercept = 1/V and X-intercept = -1/K

Step-by-step explanation:

a)

If  

[tex]\bf f(x)=\frac{K}{V}x+\frac{1}{V}[/tex]

and also

f(x) = 0.2x + 8

Then

[tex]\bf \frac{1}{V}=8\rightarrow V=\frac{1}{8}[/tex]

[tex]\bf \boxed{V=0.125}[/tex]

[tex]\bf \frac{K}{V}=\frac{K}{0.125}=0.2\rightarrow\boxed{K=0.025}[/tex]

b)

The Y-intercept is gotten when x=0, so the Y-intercept is [tex]\bf \boxed{\frac{1}{V}}[/tex]

The X-intercept is gotten when y=0 (f(x)=0) so

[tex]\bf 0=\frac{K}{V}x+\frac{1}{V}\rightarrow\frac{K}{V}x=-\frac{1}{V}\rightarrow x=-\frac{1}{K}[/tex]

and the X-intercept is  

[tex]\bf \boxed{x=-\frac{1}{K}}[/tex]

K and V written as fractions are

[tex]\bf K=\frac{25}{1000}=\frac{1}{40}[/tex]

[tex]\bf V=\frac{1}{8}[/tex]