The segments shown below could form a triangle 1 8 8

Yes. 

To form a triangle every side must be smaller in length than the sum of the two other sides. 

For example: sides denoted by a,b,c
for a triangle to form
a<b+c
b<a+c
c<a+b
Thus in the case of the Isosceles triangle with side lengths 1,8,8 the rules aforementioned are fulfilled. This means that a triangle with said side lengths can exist.

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

answer: the function g(x) has the greatest slope.