Question

if a point on the graph of a proportional relationship is located at 3,4, can you determine the constant of proportionality? explain

Answer 1

The answer is: No, because we also need to know the type of proportionality

In mathematics, we talk about proportionality when two variables are related and this relationship is that there is a constant ratio between them. There are two types of proportionality.

1. Direct Proportionality:

If there are two variables x and y, we can write the relationship between them as follows:

$y=kx$

So, by substituting the point in this equation we have that the constant of proportionality is:

$4=k(3) \\ \\ \therefore \boxed{k=\frac{4}{3}}$

2. Inverse Proportionality:

In this case, the relationship is:

$y=\frac{k}{x}$

So, the constant of proportionality is:

$4=\frac{k}{3} \\ \\ \therefore \boxed{k=12}$

As you can see, we have found two different values of the constant of proportionality. So, it is necessary to know the type of proportionality.