Ratios and Rates

NZ Level 6 (NZC) Level 1 (NCEA)

Interpreting Proportional Relationships

Lesson

We've already learnt 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.

Remember!

Proportional relationships are a special kind of linear relationship that can be written generally in the form $y=kx$`y`=`k``x` and always pass through the origin $\left(0,0\right)$(0,0).

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.

The price for playing arcade games is shown in the graph.

What does the point $\left(3,5\right)$(3,5) represent on the graph?

A) $5$5 games cost $\$3$$3 B) $3$3 games cost $\$5$$5

Think: Which variable does each axis represent?

Do:

The horizontal axis tells us the price. Since the $x$`x`-coordinate corresponds to the horizontal axis, this means the price is $\$3$$3.

Similarly, the vertical axis tells us the number of games played. The $y$`y`-coordinate corresponds to the vertical axis, so this means $5$5 games were played.

So A) $5$5 games cost $\$3$$3.

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

What does the point $\left(4,2\right)$(4,2) represent on the graph?

The number of liters of gas used by a fighter jet over a certain number of seconds is shown in the graph. What does the point on the graph represent?

Apply direct and inverse relationships with linear proportions

Apply numeric reasoning in solving problems