Question

Two graphs are shown below: graph A shows scatter points 1, 2 and 2, 2 and 3, 2 and 4, 2 and 5, 2graph A shows scatter points 1, 11 and 2, 9 and 3, 7 and 4, 5 and 5, 3 Which scatter plot shows a negative correlation between x and y? Only graph A Only graph B Both graph A and graph B Neither graph A nor graph B

Answer 1

Answer:

Option B.

Step-by-step explanation:

It is given that scatter points of graph A and graph B are

Graph A :  (1,2), (2,2), (3,2), (4,2) and (5,2).

Graph B : (1,11), (2,9), (3,7), (4,5) and (5,3).

If a line passes through two points $(x_1,y_1)$ and $(x_2,y_2)$, then the rate of change is

$m=\frac{y_2-y_1}{x_2-x_1}$

Consider any two ordered pairs of graph A: (1,2) and (2,2). Slope of graph A is

$m=\frac{2-2}{2-1}=0$

The rate of change of graph A is 0, which represents a no correlation between x and y.

Consider any two ordered pairs of graph B: (1,11) and (2,9). Slope of graph B is

$m=\frac{9-11}{2-1}=-2$

The rate of change of graph B is -2, which represents a negative correlation between x and y.

Therefore, the correct option is B.

Answer 2

Both graph a and b look at the gradients between one point then the one after it. It stays constant from one to the next. (Gradient is 2 by the way: (5-3)/(2-1))