A long string with a balloon at the end was tied to the ground. After a breeze came up, the balloon was 55 feet to the right of where it was tied and 30 feet above the ground, as shown in the figure below. What is the slope of the line between the balloon and the point where it was tied?

The slope is 0.55

Step-by-step explanation:

Right Triangles

The string, the ground, and the height of the balloon form a right triangle where the trigonometric ratios are satisfied.

The image below shows the geometric construction. We are required to find the slope the string forms with the ground.

It can be found by using the tangent ratio:

Substituting y=30 and x=55

The slope is 0.55

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: