Write and solve an equation to find the variable.

see explanation

Step-by-step explanation:

The mean of a set of data is calculated using

mean = , that is

= 7.1

37.5 + y = 7.1 ( multiply both sides by 6 )

37.5 + y = 42.6 ( subtract 37.5 from both sides )

y = 5.1

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: