Proportional vs NonProportional

Front

What is a proportional relationship?

Back

A proportional relationship is one where two quantities maintain a constant ratio, meaning that as one quantity increases or decreases, the other does so in a consistent manner.

Front

What is a non-proportional relationship?

Back

A non-proportional relationship is one where the ratio between two quantities is not constant, meaning that the relationship does not maintain a consistent rate of change.

Front

How can you identify a proportional relationship from a graph?

Back

A graph represents a proportional relationship if it is a straight line that passes through the origin (0,0).

Front

How can you identify a non-proportional relationship from a graph?

Back

A graph represents a non-proportional relationship if it is a straight line that does not pass through the origin or if it is not a straight line.

Front

What does the equation y = kx represent?

Back

The equation y = kx represents a proportional relationship, where k is the constant of proportionality.

Front

What does the equation y = mx + b represent?

Back

The equation y = mx + b represents a linear relationship, which can be proportional if b (the y-intercept) is 0, and non-proportional if b is not 0.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. If the y-intercept is not zero, the relationship is non-proportional.

Front

If a table shows the values (1, 2), (2, 4), (3, 6), is it proportional?

Back

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

Front

If a table shows the values (1, 2), (2, 5), (3, 7), is it proportional?

Back

No, it is non-proportional because the ratio of y to x is not constant.

Front

What is the constant of proportionality?

Back

The constant of proportionality is the constant factor (k) that relates two proportional quantities, found by dividing y by x.