4.10 Interpreting proportional relationships

We've already learned about proportional relationships, where two quantities vary in such a way that one is a constant multiple of the other. In other words, they always vary by the same constant.

To interpret information from a graph, we need to look at pairs of coordinates. Coordinates tell us how one variable relates to the other. Each pair has an $x$x value and a $y$y value in the form $\left(x,y\right)$(x,y).

• The $x$x-value tells us the value of the variable on the horizontal axis.
• The $y$y-value tells us the value of the variable on the vertical axis.

It doesn't matter what labels we give our axes, this order is always the same.

 

Let's look at some examples and see this in action.

 

Worked example

Question 1

The number of eggs farmer Joe's chickens produce each day are shown in the graph. 

What does the point $\left(6,3\right)$(6,3) represent on the graph?

Think:  The first coordinate corresponds to the values on the $x$x-axis (which in this problem would represent the number of days) and the second coordinate corresponds to values on the $y$y-axis ( which in this problem would represent the number of eggs).

Do: 

Using the given information in context, we can interpret this point to mean that in $6$6 days the chickens will produce $3$3 eggs.

Reflect: How many days does it take for the chickens to lay $1$1 egg?

 

Practice questions

question 2

question 3