Lesson 6 Proportional Graphs

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities when they are combined together. It expresses how much of one quantity corresponds to one unit of another quantity.

Front

How do you calculate the unit rate from a given quantity?

Back

To calculate the unit rate, divide the total quantity by the number of units. For example, if 6 cm of rain falls in 3 hours, the unit rate is 6 cm ÷ 3 hours = 2 cm per hour.

Front

What does it mean for a graph to be linear?

Back

A graph is linear if it forms a straight line when plotted on a coordinate plane, indicating a constant rate of change.

Front

What does it mean for a graph to be nonlinear?

Back

A graph is nonlinear if it does not form a straight line, indicating that the rate of change is not constant.

Front

What is a proportional relationship?

Back

A proportional relationship is one where two quantities maintain a constant ratio or rate. For example, if y is proportional to x, then y = kx for some constant k.

Front

What is a non-proportional relationship?

Back

A non-proportional relationship is one where the ratio between two quantities changes. For example, if y does not equal kx for any constant k, then y and x are non-proportional.

Front

If Jeff ran 6 miles in 4 hours, what is his speed in miles per hour?

Back

His speed is 6 miles ÷ 4 hours = 1.5 miles per hour.

Front

If a table of values shows a constant difference between y-values for equal increments of x-values, what type of relationship is it?

Back

It is a linear relationship.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while nonlinear functions have varying rates of change and do not graph as straight lines.

Front

How can you determine if a function is linear or nonlinear from a graph?

Back

If the graph forms a straight line, the function is linear. If the graph curves or has bends, the function is nonlinear.