The equation y = 1 5 x represents a proportional relationship. Explain how you can tell the relationship is proportional from the graph of the equation, and how you can find the constant of proportionality.

If you graph this, you'll see a line with slope 15 that goes through the origin. If there were a y-intercept other than zero, such as in y = 15x + 5, this equation would not represent a proportional relationship.

In summary:

There's a constant ("constant of proportionality") slope, which here is 15.

The line MUST go through the origin.

ap8997154 ap8997154 · Answer 2 · 2022-07-31T07:55:35+02:00

The given relationship is directly proportional relationship with a constant of proportionality equal to 15.

What is the 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.

For any equation to be proportional, the graph of the equation must be a slant line, therefore, the straight line must have a slope.

In the graph, a positive slope depicts that the relationship is directly proportional relationship while a negative slope of the line represents that the relationship is inversely proportional.

Also, the value of the constant of proportionality is the slope of the line. Therefore, from a graph the constant of proportionality can be calculated by calculating the slope of the graph.

For the given equation y=15x, the graph of the equation is a straight line and the slope of the line is 15, which is positive. Thus, it can be said that the given relationship is directly proportional relationship with a constant of proportionality equal to 15.

Learn more about Directly and Inversely proportional relationships:

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