Recall that a rate is a special type of ratio that is used to compare different types of quantities.
A unit rate describes how many units of the first quantity corresponds to one unit of the second quantity.
Some common unit rates are distance per hour, cost per item, earnings per week, etc. Do you see how in each example the first quantity is related to one unit of the second quantity?
When we are looking at unit rates in tables and graphs, we want to know how much the dependent (y) variable will increase when the independent (x) variable is increased by one. The change in the values of y for every change in the values of x is referred to as the slope of the line. So the slope and unit rate represent the same thing.
In a given equation that shows the proportional relationship between two variables, y=kx, k is known as the constant of proportionality. Upon inspection we can notice that k is the slope of the equation and can be rewritten as y=mx, where m is the slope of the line.
Therefore for a given proportional relationship, the unit rate, slope, and constant of proportionality are all equal.
The graph shows the amount of time it takes Kate to make beaded bracelets.
Find the slope of the line.
Interpret the unit rate based on the slope of the line.
Carl has kept a table of his reading habits which is shown below:
Number of weeks | 12 | 24 | 36 | 48 |
---|---|---|---|---|
Number of books read | 20 | 40 | 60 | 80 |
Determine the unit rate of the number of books Carl reads for every week, rounding the answer in one decimal place.
The number of cans of white and red paint needed to make 'flamingo pink' is represented by the equation y = 10 x where x is the number of cans of red paint and y is the number of cans of white paint needed.
Based on the equation, how many cans of white paint are needed for every can of red paint?
A unit rate describes how many units of the first quantity corresponds to one unit of the second quantity.
When we are looking at unit rates on a graph, we want to know how much the dependent (y) variable will increase when the independent (x) variable is increased by one.
In a proportional relationship, the unit rate, slope, and constant of proportionality are all equal.