Proportional Reasoning

Front

What is proportional reasoning?

Back

Proportional reasoning is the ability to compare ratios and understand the relationship between quantities that change in relation to each other.

Front

What does it mean for a table to be proportional?

Back

A table is proportional if the ratios of the values in the table are constant.

Front

What is the constant of proportionality?

Back

The constant of proportionality is the constant value (k) that relates two proportional quantities, often represented as y = kx.

Front

How can you identify a proportional relationship in a graph?

Back

A proportional relationship in a graph is identified by a straight line that passes through the origin (0,0).

Front

What does it mean if a graph is not proportional?

Back

If a graph is not proportional, it means that the relationship between the variables does not maintain a constant ratio.

Front

If the constant of proportionality is 8, what is the relationship between x and y in the equation y = 8x?

Back

For every increase of 1 in x, y increases by 8.

Front

How do you find 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.

Front

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

Back

An example of a proportional relationship is the cost of apples if they are sold at a constant price per pound.

Front

If a table shows the values (2, 4), (4, 8), (6, 12), is it proportional?

Back

Yes, because the ratio of y to x is constant (2:1).

Front

What is the formula for finding the constant of proportionality?

Back

The formula is k = y/x, where k is the constant of proportionality.