Question

the speed a car travels is inversely proportional to the time it takes to complete a 100 mile trip. which of the following graphs best represents this situation

Answer 1

Inversely proportion states that a relationship between two variables in which the product is a constant.

If one of the variable increases, then the other decreases in proportion so that the product is unchanged.

If y is inversely proportional to x, then the equation is of the form

`y = (k)/(x)` ; where k is the constant proportionality.

As per the given condition: Speed of a car is inversely proportional to the time it takes to complete a 100 mile trip,

Let x represents the speed of car and y represents the time taken.

From the given condition:

`x \propto (1)/(y)`

Then by definition of inversely proportional;

`x = (k)/(y)` [Since,
`speed = (Distance)/(Time)` ]

Here, k represents the distance(i.e constant) = 100 miles.

therefore, the equation becomes now;

`x = (100)/(y)` or

xy = 100

The following graph for the above equation as shown below :