Answer:
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
[tex]y = \frac{k}{x}[/tex] ; 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:
[tex]x \propto \frac{1}{y}[/tex]
Then by definition of inversely proportional;
[tex]x = \frac{k}{y}[/tex] [Since, [tex]speed = \frac{Distance}{Time}[/tex] ]
Here, k represents the distance(i.e constant) = 100 miles.
therefore, the equation becomes now;
[tex]x = \frac{100}{y}[/tex] or
xy = 100
The following graph for the above equation as shown below :
