direct variation

Front

What is direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other, expressed as y = kx, where k is the constant of proportionality.

Front

How do you find the constant of proportionality in a direct variation problem?

Back

To find the constant of proportionality (k), divide the value of y by the value of x (k = y/x) when given a pair of values.

Front

If a person weighs 90 kg and contains 60 kg of water, what is the constant of proportionality for water content?

Back

The constant of proportionality is k = 60 kg / 90 kg = 0.67.

Front

How do you solve for an unknown in a direct variation equation?

Back

To solve for an unknown, use the formula y = kx, substituting known values for y, k, or x to find the missing variable.

Front

What is the formula for direct variation?

Back

The formula for direct variation is y = kx, where y varies directly with x.

Front

In the context of pay, if a worker earns $70 for 5 hours, how much do they earn per hour?

Back

To find the hourly wage, divide the total pay by the number of hours: $70 / 5 hours = $14 per hour.

Front

If a person works 31 hours and earns $190.65, what is the constant of proportionality for their pay?

Back

The constant of proportionality is k = $190.65 / 31 hours = $6.14 per hour.

Front

What is the relationship between hours worked and pay in a direct variation scenario?

Back

In a direct variation scenario, pay increases proportionally with the number of hours worked.

Front

How can you express a direct variation relationship in a graph?

Back

In a graph, a direct variation relationship is represented by a straight line that passes through the origin (0,0).

Front

What does it mean if two quantities vary directly?

Back

If two quantities vary directly, it means that as one quantity increases, the other quantity increases at a constant rate.