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. It can be expressed as y = kx, where k is a non-zero constant.

Front

What does the equation y = 2x + 3 indicate about direct variation?

Back

This equation does not represent direct variation because it includes a constant term (3) that shifts the line up, meaning it does not pass through the origin.

Front

What is the graph of a direct variation?

Back

The graph of a direct variation is a straight line that passes through the origin (0,0).

Front

What is the condition for two variables to show direct variation?

Back

For two variables to show direct variation, their ratio must remain constant as one variable changes.

Front

If y = 5x, do x and y show direct variation?

Back

Yes, because it can be expressed in the form y = kx, where k = 5.

Front

What is the significance of the constant k in direct variation?

Back

The constant k represents the rate of change or the proportionality constant between the two variables.

Front

Can direct variation have a negative constant?

Back

Yes, direct variation can have a negative constant, which means that as one variable increases, the other decreases.

Front

Write an equation for the direct variation where y is 1/4 of x.

Back

y = 1/4x.

Front

What happens to the graph of a direct variation if k is negative?

Back

The graph will still be a straight line passing through the origin, but it will slope downwards from left to right.

Front

What is the relationship between direct variation and proportionality?

Back

Direct variation is a specific type of proportional relationship where the ratio of y to x is constant.