Test the set of functions for linear independence in ℱ. If it is linearly dependent, express one of the functions as a linear combination of the others. (If the set is linearly independent, enter INDEPENDENT. If the set is linearly dependent, enter your answer as an equation using the variables f, g, and h as they relate to the question.) {f(x) = 8, g(x) = sin(x), h(x) = cos(x)}

Linearly independent

Step-by-step explanation:

let a,b,c be element of F. for all x element of F.

1) if a, b and c are zero then they are independent

2) if not all a,b,c are zero then it is independent.

Now lets write it as a linear combination

 i.e  8a +b Sinx +c Cosx = 0

equating the coefficients we have

: 8a =0 hence a = 0

: b Sinx = 0

b = 0

: c Cos x = 0

c is not 0

Hence it is Linearly independent

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is