Check for Understanding

Front

What does it mean for a relationship to be proportional?

Back

A proportional relationship means that two quantities maintain a constant ratio, or that one quantity is a constant multiple of the other.

Front

How can you identify a proportional relationship from a graph?

Back

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

Front

What is the constant of proportionality?

Back

The constant of proportionality (k) is the constant factor that relates two proportional quantities, expressed in the equation y = kx.

Front

If k = 30, what is the equation of the proportional relationship?

Back

The equation is y = 30x.

Front

What is the formula for a proportional relationship?

Back

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

Front

How do you find the constant of proportionality from a table of values?

Back

To find the constant of proportionality from a table, divide the value of y by the corresponding value of x for any pair of values.

Front

If y = 15x, what is the constant of proportionality?

Back

The constant of proportionality is k = 15.

Front

What is the significance of the point (0,0) in a proportional relationship?

Back

The point (0,0) indicates that when x is zero, y is also zero, which is a characteristic of proportional relationships.

Front

Can a proportional relationship be represented by a nonlinear graph?

Back

No, a proportional relationship must be represented by a linear graph that passes through the origin.

Front

What happens to the graph of a proportional relationship if the constant of proportionality is negative?

Back

If the constant of proportionality is negative, the graph will still be a straight line through the origin, but it will slope downwards.