Direct Variation and Proportional Relationships

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 is a Proportional Relationship?

Back

A proportional relationship is a relationship between two quantities where their ratio is constant. This means that as one quantity increases, the other quantity increases at a consistent rate.

Front

What does it mean if a table is non-proportional?

Back

A non-proportional table shows values that do not maintain a constant ratio. This means that the relationship between the two variables is not consistent.

Front

How can you identify a direct variation from a graph?

Back

A graph represents direct variation if it is a straight line that passes through the origin (0,0).

Front

What is the y-intercept in a graph?

Back

The y-intercept is the point where the graph crosses the y-axis. It represents the value of y when x is 0.

Front

If y = 39 when x = 3, what is the constant of variation (k)?

Back

k = y/x = 39/3 = 13.

Front

What is the equation of a direct variation?

Back

The equation of a direct variation is y = kx, where k is the constant of variation.

Front

What does a non-proportional graph look like?

Back

A non-proportional graph is a straight line that does not pass through the origin or a curve that does not maintain a constant ratio.

Front

If y = 3.75x + 2, is this a direct variation?

Back

No, it is non-proportional because of the +2, which is the y-intercept.

Front

How do you find the value of y in a direct variation if x is given?

Back

Use the formula y = kx, substituting the value of x and the constant k.