Part A:
In order to find the slope of [tex]f(x)[/tex] we can use the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
So, using first two pairs from the given table we have:
[tex]m=\frac{-10-(-15)}{0-(-1)}=\frac{-10+15}{1}=\frac{5}{1}=5[/tex]
Every linear function has the following general look:
[tex]y=mx+b[/tex], where [tex]m[/tex] is the slope of the function.
Applying that general look to our function [tex]g(x)[/tex] we see that it's slope equals 2.
So, we can say that value of [tex]f(x)[/tex] is growing two and half more times faster then value of [tex]g(x)[/tex] as their slopes' ratio is 5:2.
Part B:
The y-intercept of function is it's value in case x is equal 0.
Using the given table we find that the y-intercept of [tex]f(x)=-10[/tex]
As for [tex]g(x)[/tex], let's substitute x value with 0 and solve the equation:
[tex]g(x)=2\cdot0+8=8[/tex]
So, the function [tex]g(x)[/tex] has greater y-intercept then function [tex]f(x)[/tex].
