Graphs of proportional relationships

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other quantity is constant.

Front

How do you identify a proportional relationship from a graph?

Back

A proportional relationship can be identified on a graph as a straight line that passes through the origin (0,0).

Front

What is the constant of proportionality?

Back

The constant of proportionality is the constant ratio between two proportional quantities, often represented as 'k' in the equation y = kx.

Front

If y varies directly with x, what is the equation that represents this relationship?

Back

The equation is y = kx, where k is the constant of proportionality.

Front

How do you find the constant of proportionality from given values of x and y?

Back

To find the constant of proportionality, divide the value of y by the value of x (k = y/x).

Front

What does the slope of a line represent in a proportional relationship?

Back

The slope of a line in a proportional relationship represents the constant of proportionality.

Front

If you can buy 5 shirts for $60, what is the cost of 2 shirts?

Back

Using the proportion, the cost of 2 shirts can be found using the equation (5/60) = (2/c), which gives c = $24.

Front

What is the formula to calculate the slope of a line?

Back

The formula to calculate the slope (m) of a line is m = (change in y) / (change in x).

Front

What is the significance of the origin in a proportional relationship graph?

Back

The origin (0,0) signifies that when one quantity is zero, the other quantity is also zero, indicating a direct relationship.

Front

How can you express a proportional relationship using a table?

Back

A proportional relationship can be expressed in a table by listing pairs of values (x, y) that maintain a constant ratio.