# Find f(g(x)) for f(x)=-3x-6 and g(x)=-1/2x+3 and the equation of the line through points (10,12) and (16,14)?

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The functions f(x) and g(x) are defined by f(x) =-3x-6 and g(x)=(-1/2)*x+3

f(g(x)) = f((-1/2)*x+3)

= -3*((-1/2)*x+3) - 6

= (3/2)*x - 9 - 6

= (3x)/2 - 15

The equation of a line through points (x1, y1) and (x2, y2) is given by:

`(y - y2)/(x - x2) = (y1 - y2)/(x1 - x2)`

For the points (10,12) and (16,14), x1 = 10, x2 = 16, y1 = 12 and y2 = 14. The equation of the line between these points is:

`(y - 14)/(x - 16) = (12 - 14)/(10 - 16)`

`(y - 14)/(x - 16) = (-2)/(-6)`

(y - 14)*6 = (x - 16)*2

6y - 84 = 2x - 32

2x - 6y + 52 = 0

f(x)=-3x-6

g(x)=(-1/2)x+3

f(g(x))=f((-1/2)x+3)

=-3((-1/2)x+3)-6

=(3/2)x-9-6

=(3/2)x-15

Equation of line through points (10,12) and (16,64)

`y-12=((64-12)/(16-10))(x-10)`

`y-12=(52/6)(x-10)`

`3(y-12)=26(x-10)`

`3y-36=26x-260`

`26x-3y=260-36`

`26x-3y=224`