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

Option B.

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=(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=(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=(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.