Two variables are correlated with r = -0.23. which description best describes the strength and direction of the association between the variables?

Negative and weak correlation

Step-by-step explanation:

Correlation is another word for association. If there is a positive association between two variables, i.e. whenever x increases y decreases then we will have covariance (x,y) as positive and hence correlation also positive

Correlation denoted by r lies between -1 and 1

If |r| is nearer to 1, we say strong correlation otherwise weak correlation

Two variables x and y are said to have correlation as -0.23

Since 0.23 is nearer to 0 than to 1 we say they are weakly correlated

Since r has a negative sign, we find that the two variables are negatively correlated and also weak.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: