Find the midpoint of the line segment joining the points (10, 13) and (−7, 7).

(8.5, 3)

(1.5, 3)

(1.5, 10)

(8.5, 10)

Let the midpoint be (x,y). We can find it by using the midpoint formula.

(x,y) = (, )

(x,y) = (,)

(x,y) = (1.5,10)

Thus, the midpoint is (1.5,10).

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: