Linear Relations

Lesson

We've already learnt about the concept of a unit rate, which describes how many units of the first type of quantity corresponds to one unit of the second type of quantity.

Now we are going to look at how to compare unit rates, which is a very helpful skill because, for one thing, it can help us work out the best deal on any item we may want to buy.

Basically, when we compare unit rates, we are making a judgement about the characteristics of rates, whether it be which item is the best value (ie. the lowest cost per unit of product) or which line on a graph has greater unit rate.

Handy Hints for Finding Unit Rates

To find the unit rate:

- from a table or equation, find the constant of proportionality (this will be the unit rate).
- from a graph, find the slope of the line. The value of the slope will be your unit rate.

Let's check out some examples below.

Which of the following relationships has the higher unit rate?

$c=10w$

`c`=10`w`ALoading Graph...B$c=10w$

`c`=10`w`ALoading Graph...B

Valentina wants to buy candles. Select the option from the following that offers the best value.

Buy $13$13 candles for $\$18.72$$18.72.

ABuy $4$4 candles for $\$3.52$$3.52.

BBuy $13$13 candles for $\$18.72$$18.72.

ABuy $4$4 candles for $\$3.52$$3.52.

B

Determine, through investigation, that the rate of change of a linear relation can be found by choosing any two points on the line that represents the relation, finding the vertical change between the points (i.e., the rise) and the horizontal change between the points (i.e., the run), and writing the ratio