On these questions about slopes on graphs

  a) {C, D}, {B, E}, A . . . . four possible equivalent answers (explanation below)

  b) Line C shows a "directly proportional" relationship

Step-by-step explanation:

Slope is the ratio of "rise" (vertical change) to "run" (horizontal change). Positive changes are "up" and "right".

Line A -- has no vertical change, so its slope is 0.

Line B -- changes 1 unit vertically for each 4 units horizontally, so its slope is 1/4.

Line C -- changes 1 unit vertically for each 2 units horizontally, so its slope is 1/2.

Line D -- changes 1 unit vertically for each 2 units horizontally, so its slope is 1/2. This is the same slope as line C, so neither is greater than the other.

Line E -- changes 1 unit vertically for each 4 units horizontally, so its slope is 1/4. This is the same slope as line B, so neither is greater than the other.

If we use alphabetical order to rank equal slopes, then the slopes (greatest to least) are ...

  C (1/2), D (1/2), B (1/4), E (1/4), A (0)

A "directly proportional" relationship graphs as a straight line through the origin. The only line passing through the point where the x- and y-axes meet is line C.

  Line C represents a proportional function.

  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).

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05