In a directly proportional relationship, increasing one variable will increase another. It is not a proportional relationship graph.
What is a directly proportional and inversely proportional relationship?
Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
p = kq
where k is some constant number called the constant of proportionality.
This directly proportional relationship between p and q is written as
p∝q where that middle sign is the sign of proportionality.
In a directly proportional relationship, increasing one variable will increase another.
Now let m and n be two variables.
Then m and n are said to be inversely proportional to each other if
[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]
(both are equal)
where c is a constant number called the constant of proportionality.
This inversely proportional relationship is denoted by
[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
A proportional relationship is a relationship in which the value of one variable changes with the change in another variable. This change is always in a fixed ratio. Thus, when the relationship is plotted on the graph it creates a straight line and all the data points lie on this line.
Since in the graph made by Jay the line is not able to connect all the data points, it is not a proportional relationship graph.
Learn more about Directly inversely proportional relationships:
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