Pro & Non Functions, Unit Rate, Direction Variation

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 is constant. This means that as one quantity increases or decreases, the other quantity does so in a consistent manner.

Front

How do you determine the slope of a line in a graph?

Back

The slope of a line is determined by the change in the y-values divided by the change in the x-values (rise over run). It represents the rate of change between the two variables.

Front

What does it mean for a graph to represent y as a function of x?

Back

A graph represents y as a function of x if for every x-value, there is exactly one corresponding y-value. This means that no vertical line can intersect the graph at more than one point.

Front

What is the unit rate?

Back

The unit rate is a ratio that compares a quantity to one unit of another quantity. It is often expressed as 'per one' and is useful for understanding the cost or rate of something.

Front

How can you find the cost per item when given the total cost and quantity?

Back

To find the cost per item, divide the total cost by the number of items. For example, if 6 pencils cost 30 cents, the cost per pencil is 30 cents / 6 = 5 cents.

Front

What is direct variation?

Back

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

Front

What is a non-proportional relationship?

Back

A non-proportional relationship is a relationship between two quantities that does not maintain a constant ratio. This means that the graph of the relationship does not pass through the origin.

Front

How do you identify a non-function from a graph?

Back

A graph is identified as a non-function if a vertical line drawn through the graph intersects it at more than one point, indicating that a single x-value corresponds to multiple y-values.

Front

What is the significance of the origin in a graph?

Back

The origin (0,0) is significant in graphs of proportional relationships because it indicates that when one quantity is zero, the other quantity is also zero. If a graph does not pass through the origin, it represents a non-proportional relationship.

Front

How do you calculate the cost for a different quantity using direct variation?

Back

To calculate the cost for a different quantity using direct variation, set up a proportion based on the known cost and quantity, and then solve for the unknown cost.