Respuesta :
Answer:
The required function is: [tex]f(x)=\frac{0.025}{0.125}x +\frac{1}{0.125}[/tex]
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).
Step-by-step explanation:
Consider the provided function.
Part (A)
It is given that the function is [tex]f(x)=0.2x+8[/tex]
We need to change the formula in [tex]f(x)=\frac{K}{V}x +\frac{1}{V}[/tex]
By the comparison we can say that
[tex]\frac{1}{V}=8[/tex]
[tex]V=\frac{1}{8}=0.125[/tex]
Also by the compression,
[tex]0.2=\frac{K}{V}[/tex]
[tex]0.2=\frac{K}{0.125}[/tex]
[tex]K=0.025[/tex]
Substitute the value of V and K in [tex]f(x)=\frac{K}{V}x +\frac{1}{V}[/tex]
The required function is: [tex]f(x)=\frac{0.025}{0.125}x +\frac{1}{0.125}[/tex]
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 [tex]y=\frac{K}{V}x +\frac{1}{V}[/tex]
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 [tex]y=\frac{K}{V}x +\frac{1}{V}[/tex] to find x intercept.
[tex]0=\frac{K}{V}x +\frac{1}{V}[/tex]
[tex]-\frac{1}{V}=\frac{K}{V}x [/tex]
[tex]Kx=-1[/tex]
[tex]x=\frac{-1}{K}[/tex]
Therefore, the x-intercept of the line is the point (-1/K, 0).
