Pleas help me with my math class

The value of the constant is 0.8

Explanation:

The graph has the following properties:

Horizontal-axis (independent variable): width

Vertical-axis (dependent variable): height

Points on the curve:

       (0.5, 1.6), (0.8, 1), (1.6, 0.5), and (2, 0.4)

The equation represented by the graph is an inverse variation:

Height = constant / width.

From that equation, you can solve for the contstant:

constant = height × width

Now, you can take any ordered pair to find the constant:

(0.5, 1.6) ⇒ constant = 0.5 × 1.6 = 0.8

(0.8, 1) ⇒constant = 0.8 × 1 = 0.8

(1.6, 0.5) ⇒ constant = 1.6 × 0.5 = 0.8

(2, 0.04) ⇒ constant = 2 × 0.4 = 0.8

Thus, you have obtained that the constant is 0.8.

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: