Functions and Proportional vs. Non-Proportional

Front

What is the equation form of a proportional relationship?

Back

y = kx, where k is a constant.

Front

What is a non-proportional relationship?

Back

A relationship where the ratio between variables is not constant, often represented by equations like y = mx + b.

Front

Does a proportional relationship pass through the origin?

Back

Yes, a proportional relationship always passes through the origin (0,0).

Front

What is direct variation?

Back

A relationship where one variable is a constant multiple of another, expressed as y = kx.

Front

If y = 39 when x = 3, what is y when x = 2 in a direct variation?

Back

y = 26.

Front

What does it mean if a graph does not pass through the origin?

Back

It indicates a non-proportional relationship.

Front

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

Back

Check if the ratios of y to x are constant for all pairs.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the constant of proportionality?

Back

The constant k in the equation y = kx, representing the ratio of y to x.

Front

Give an example of a proportional relationship in real life.

Back

The cost of apples at a store where each apple costs the same amount.