Proportionality in Tables, Graphs, and Equations

Front

What is the constant of proportionality?

Back

The constant of proportionality is the ratio between two proportional quantities, indicating how much one quantity changes in relation to another. For example, if y = kx, then k is the constant of proportionality.

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 has a constant slope, indicating a consistent ratio between the x and y values.

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities when they are combined together. It expresses how much of one quantity corresponds to one unit of another quantity, such as 2 cm per hour.

Front

If 3 pounds of hamburger costs $6, what is the cost per pound?

Back

The cost per pound is $2, calculated by dividing the total cost by the number of pounds: $6 ÷ 3 pounds = $2 per pound.

Front

How do you solve a proportion?

Back

To solve a proportion, cross-multiply the two ratios and set them equal to each other. For example, if a/b = c/d, then ad = bc.

Front

What is the formula for finding the constant of proportionality from a table?

Back

To find the constant of proportionality from a table, divide the y-value by the corresponding x-value for any pair of values. If the ratio is constant, the relationship is proportional.

Front

What is an example of a proportional relationship in real life?

Back

An example of a proportional relationship is the speed of a car. If a car travels 60 miles in 1 hour, it will travel 120 miles in 2 hours, maintaining a constant speed.

Front

What does it mean if a table shows non-proportional relationships?

Back

A table shows non-proportional relationships if the ratios of the y-values to the x-values are not constant, meaning the relationship does not maintain a consistent rate.

Front

How can you identify a proportional relationship from a graph?

Back

You can identify a proportional relationship from a graph by checking if the line is straight and passes through the origin (0,0). If it does, the relationship is proportional.

Front

What is the relationship between unit rates and constant of proportionality?

Back

The unit rate is the constant of proportionality expressed as a ratio of one unit of the first quantity to the second quantity, showing how much of the second quantity corresponds to one unit of the first.