Ratios and Rates

UK Secondary (7-11)

Plotting Pairs of Ratios on Coordinate Plane

Lesson

We've already learnt about number planes, which are also called Cartesian planes or coordinate planes.

Just to recap, a number plane is created by two perpendicular lines that we call an $x$`x`-axis and a $y$`y`-axis.

The **$x$ x-axis** is the

Where the two axes cross each other is labelled the origin. It has a zero value on both axes.

Both axes have positive and negative values which are divided by the origin as shown in the diagram below.

We can create a grid from the $2$2 number lines. When labeling points on the grid, we always use the $x$`x`-value first.

A ratio compares the relationship between two values. It compares how much there is of one thing compared to another. We can also plot pairs of ratios on a number plane. It's a very similar process.

- The first number in a ratio becomes the $x$
`x`-value on the number plane. - The second number in that ratio becomes the $y$
`y`-value on a number plane.

For example, if I wanted to plot the ratio $3:19$3:19 on a number plane, I would plot the coordinate $\left(3,19\right)$(3,19). The green dot in the diagram below shows that coordinate. In other words, the $x$`x` value is $3$3 and the $y$`y` value is $19$19.

Plot $13:9$13:9 on the coordinate plane.

Plot $13:17$13:17 on the coordinate plane.

Consider the given graph.

a) What ratio has been plotted?

b) Which option could be being represented by this graph and ratio?

A) For every 2 green sweets in a mix, there is 1 red sweet.

B) For every 1 green sweet in a mix, there are 2 red sweets.