Question

Biochemists studying enzyme kinetics encounter formulas of the form fx)(K/V+ 1/V, where K and V are constants. Use this information to answer parts (a) and (b). (a) If f(x) 0.2x+ 8, find K and V so that fix) 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/Vx+1/V (in terms of K and V). (a) K0.025 (Simplify your answer. Type an integer or a fraction.)

Answer 1

The required function is:
`f(x)=(0.025)/(0.125)x +(1)/(0.125)`

And the value of V and K are 0.125 and 0.025 respectively.

The y intercept is 1/V or the y-intercept of the line is the point (0,1/V).

The x-intercept of the line is the point (-1/K, 0).

Explanation:

Consider the provided function.

Part (A)

It is given that the function is
`f(x)=0.2x+8`

We need to change the formula in
`f(x)=(K)/(V)x +(1)/(V)`

By the comparison we can say that

`(1)/(V)=8`

`V=(1)/(8)=0.125`

Also by the compression,

`0.2=(K)/(V)`

`0.2=(K)/(0.125)`

`K=0.025`

Substitute the value of V and K in
`f(x)=(K)/(V)x +(1)/(V)`

The required function is:
`f(x)=(0.025)/(0.125)x +(1)/(0.125)`

And the value of V and K are 0.125 and 0.025 respectively.

Part (A)

Now we need to find x-intercept and y-intercept of the line
`y=(K)/(V)x +(1)/(V)`

The above equation is in slope intercept form: y=mx+c

Where m is slope and c is y intercept.

Thus, the y intercept is 1/V or the y-intercept of the line is the point (0,1/V)

Substitute y = 0 in
`y=(K)/(V)x +(1)/(V)` to find x intercept.

`0=(K)/(V)x +(1)/(V)`

`-(1)/(V)=(K)/(V)x`

`Kx=-1`

`x=(-1)/(K)`

Therefore, the x-intercept of the line is the point (-1/K, 0).