In a proportional relationship, the values for one quantity are each multiplied by the same number to get the values for the other quantity. This number is called the constant of proportionality.

In this example, the constant of proportionality is 3.

Two quantities have a linear relationship when:

• One quantity changes by a set amount, whenever the other quantity changes by a set amount.
• The rate of change is constant.
• The graph of the relationship is a line.

This graph shows a linear relationship between number of days and number of pages read.

When the number of days increases by 2, the number of pages read always increases by 60. The rate of change is constant, 30 pages per day.

A negative association is a relationship between 2 quantities where one tends to decrease as the other increases. In a scatter plot, the data points tend to group around a line with negative slope.

This scatter plot shows a negative association between the the price of a book and the number of books sold.

An outlier is a data value that is far from the other values in the data set.

This scatter plot shows 1 outlier.

A scatterplot. Horizontal, from 20 to 32, by 2's, labeled foot length in centimeters. Vertical, from 7 to 12, by 1’s, labeled foot width in centimeters. 20 dots trend upward and to the right. Line drawn, trends linearly upward and right with 11 dots above lie and 9 below. No dots lie on the line. The line begins at about point 21 point 9 comma 9 and ends at about 31 point 25 comma 11 point 5.

A positive association is a relationship between 2 quantities where one tends to increase as the other increases. In a scatter plot, the data points tend to group around a line with positive slope.

This scatterplot shows a positive association between dog height and dog weight.

The rate of change is the amount changes when increases by 1. On a graph, the rate of change is the slope of the line.

In this graph, increases by 15 dollars when increases by 1 hour. The rate of change is 15 dollars per hour.

Graph, horizontal axis, x, amount earned in hours. vertical axis, y, amount earned in dollars. line starting at 0 comma 10, passing through 2 comma 40 and 60 comma 100.

The relative frequency of a category tells the proportion at which the category occurs in the data set. It is written as a fraction, decimal, or percentage of the total number.

For example, there were 21 dogs in a park. This table shows the frequency and the relative frequency of each color. 

A scatter plot is a graph that shows values of 2 variables on a coordinate plane. It can be used to look for relationships between the 2 variables.

Each point on this scatter plot represents the height and weight of 1 dog.

A segmented bar graph shows categories within a data set. Each whole bar represents all the data in one main category. Each bar is separated into parts (segments) that show subcategories.

Stacked bar graph in blue and yellow stripes. Horizontal labeled 10 to 12 years old, 13 to 15 years old and 16 to 18 years old. Vertical labeled 0 to 100, by 25's. Blue section means has cell phone. Yellow stripes means has no cell phone.

This segmented bar graph shows the percentage of people in different age groups that do and do not have a cell phone. For example, among people ages 10 to 12, about 40% have a cell phone and 60% do not.

A solution to an equation with 2 variables is a pair of values for the variables that make the equation true.

For example, one solution to the equation is . Substituting 6 for and 0 for makes this equation true because .

A system of equations is a set of 2 or more equations. Each equation has 2 or more variables. A solution to the system is values for the variables that make all the equations true.

These equations make up a system of equations:

The solution to this system is and . When these values are substituted for and , both equations are true: and .

A two-way table shows data for 2 categorical variables. One variable is shown in rows and the other in columns. Each entry is the frequency or relative frequency of the category shown by the column and row headings.

This two-way table shows the results of a study. The study looked at how meditation affects the way athletes feel.