3.04 Equivalent ratios on the coordinate plane
Each column in a table of values such as a ratio table may be grouped together in the form $$(x,y). We call this pairing an ordered pair, which represents a specific location in the coordinate plane. We can use the ordered pairs in a ratio table to represent equivalent ratios as graphs in the coordinate plane.
Exploration
Let's consider the following table of values that represents the ratio of $$x:y as $$1:3.
| $$x | $$1 | $$2 | $$3 | $$4 |
|---|---|---|---|---|
| $$y | $$3 | $$6 | $$9 | $$12 |
The table of values has the following ordered pairs:
$$(1,3),(2,6),(3,9),(4,12)
We can plot each ordered pair as a point on the $$xy-plane.
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However, there are many more pairs of $$x and $$y values that satisfy the ratio of $$1:3. In fact, there are an infinite amount of pairs!
To represent all the values in between whole numbers that represent the same ratio, we can graph a line through any two of the points.
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The graph of a ratio between two quantities is a straight line. It passes through the origin and all points found in its ratio table.
Practice questions
Question 1
The ratio of $$x:y in a proportional relationship is $$1:3.
Complete the table of values below:
$$x $$1 $$2 $$3 $$4 $$y $$ $$ $$ $$ Plot the points in the table of values.
Loading Graph...Draw the graph of the proportional relationship between $$xand $$y.
Loading Graph...
QUESTION 2
Valerie wants to make sweet and salty popcorn. She has decided the perfect mix is $$8:$$5 sweet to salty.
Complete the ratio table:
sweet ($$x) $$0 $$8 $$16 $$24 $$32 $$80 salty ($$y) $$ $$ $$ $$ $$ $$ Plot the ratio on the number plane.
Loading Graph...
Question 3
Consider the following graph:
Which of the following could be represented by this graph and ratio?
For every $$1 green sweet in a mix, there are $$2 red sweets.
AFor every $$2 green sweets in a mix, there is $$1 red sweet.
BWhat is the ratio of $$x to $$y in this plotted line?
$$2:1
A$$1:2
B