What line represents the relationship between r and s shown in the table?

The third option.

Step-by-step explanation:

You can write the following equation of the line of the exercise:

Where:

y=s

x=r

m is the slope.

b is  the intersection of the line with the y-axis (Identified as "s").

The slope can be calculated as following:

As you can see in the graph, when r=0, s=10, therefore, the intersection of the line with the y-axis (Identified as "s") is:

b=10

Therefore, the equation is:

Then, you must look for a graph that has a slope 1 and that the line intersects the y-axis (Identified as "s") at 10 (r=0, s=10)

This would be the third graph.

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).