Question

studying enzyme kinetics encounter formulas of the form f(x) = (K/V)x+1/V, where and are constants. Use this infombon to answer parts and (b). (a) If f(x) = 0.9x + 10, find K and V so that f(x) may be written in the form f(x) = (K/V)x+ 1/V. (b) Find the x-intercept and y-intercept of the line y - (K/V)x+1/V (in terms of K and V). (a) K= (Simplify your answer. Type an integer or a fraction.)

Answer 1

Answer:

a)  K = 0.09, V = 0.1

b)

$y-intercept= \displaystyle\frac{1}{V}$

$x-intercept= -\displaystyle\frac{1}{K}$

Step-by-step explanation:

We are given that:

$f(x) = \displaystyle\frac{K}{V}x + \displaystyle\frac{1}{V}$

a) If we compare the above equation with the given equation:

$f(x) = 0.9x +10$, then, we get:

$\displaystyle\frac{1}{V} = 10\\\\V = \displaystyle\frac{1}{10} = 0.1\\\\\displaystyle\frac{K}{V} = 0.9\\\\K\times \displaystyle\frac{1}{0.1} = 0.9\\\\K = 0.09$

K = 0.09, V = 0.1

b) $f(x) = \displaystyle\frac{K}{V}x + \displaystyle\frac{1}{V}$

y-intercept is the value when x = 0. Putting x = 0,

$y-intercept= \displaystyle\frac{1}{V}$

x-intercept is the value when y = 0. Putting y = 0, we get,

$0 = \displaystyle\frac{K}{V}x + \displaystyle\frac{1}{V}\\\\x = \displaystyle\frac{V}{K}\times -\displaystyle\frac{1}{V}\\\\x = -\displaystyle\frac{1}{K}$