Proportional Tables and Graphs

Front

What is the constant ratio or constant of proportionality?

Back

The constant ratio or constant of proportionality is the ratio between two quantities that remain constant when the quantities are proportional. For example, if a car travels 45 miles in 1 hour, the constant of proportionality is 45 miles per hour.

Front

How do you find the unit rate from a given cost?

Back

To find the unit rate, divide the total cost by the number of units. For example, if 3 pounds of apples cost $3.60, the unit rate is $3.60 ÷ 3 = $1.20 per pound.

Front

What does it mean for a graph to be proportional?

Back

A graph is proportional if it passes through the origin (0,0) and the relationship between the two variables is linear, meaning they have a constant ratio.

Front

How can you determine if a table represents a proportional relationship?

Back

A table represents a proportional relationship if the ratios of the corresponding values are constant. For example, if the ratio of y to x is the same for all pairs, the relationship is proportional.

Front

What is a coordinate point? Give an example.

Back

A coordinate point is a pair of numbers that define a position on a graph, represented as (x,y). For example, (4,4) indicates a point where x is 4 and y is 4.

Front

What is the formula for finding the constant of proportionality?

Back

The formula for finding the constant of proportionality is k = y/x, where k is the constant, y is the dependent variable, and x is the independent variable.

Front

What is a proportional table?

Back

A proportional table lists pairs of numbers that maintain a constant ratio. For example, a table showing the relationship between hours worked and money earned can be proportional if the earnings double with each additional hour.

Front

How do you identify a non-proportional relationship in a graph?

Back

A non-proportional relationship in a graph does not pass through the origin and does not maintain a constant ratio between the variables.

Front

What is the significance of the origin in proportional relationships?

Back

The origin (0,0) is significant in proportional relationships because it indicates that when one quantity is zero, the other quantity is also zero, reflecting a direct relationship.

Front

What is the unit rate of 60 miles in 2 hours?

Back

The unit rate is 60 miles ÷ 2 hours = 30 miles per hour.