Proportional Relationships/Direct Variation

Front

What is a direct variation?

Back

A direct variation is a relationship between two variables where one variable is a constant multiple of the other. It can be expressed in the form y = kx, where k is a non-zero constant.

Front

What is the equation of direct variation when k = 4?

Back

y = 4x

Front

What does it mean if a graph is proportional?

Back

A graph is proportional if it is linear and passes through the origin (0,0).

Front

Write the direct variation equation for the relationship where y = 3 when x = 1.

Back

y = 3x

Front

What is the constant of variation in the equation y = rac{1}{4}x?

Back

The constant of variation is rac{1}{4}.

Front

If y = 7x + 3, is this a proportional relationship?

Back

No, because it does not pass through the origin.

Front

How do you determine if a table of values represents a proportional relationship?

Back

Check if the ratio of y to x is constant for all pairs of values.

Front

What is the direct variation equation for a situation where 10 gallons of water are used for 2 loads of dishes?

Back

y = 5x

Front

If y = 0.5x, what is the value of y when x = 8?

Back

y = 4.

Front

What is the slope of the line represented by the equation y = 3x?

Back

The slope is 3.