Direct Variation and Graph Interpretation

The video tutorial explains the concept of direct variation, where two quantities change together in the same direction. It uses examples like calorie intake and weight gain to illustrate this relationship. The tutorial also demonstrates how to graph direct variation using simple numbers and how to transform curves into straight lines for easier analysis. The importance of straight lines in making predictions through extrapolation and interpolation is highlighted.

What does direct variation imply about the relationship between two quantities?

• They remain constant.

• They change in opposite directions.

• One increases while the other decreases.

• They change together in the same direction.

What does the term 'proportionality' refer to in the context of the video?

• A constant difference between two quantities

• A constant ratio between two quantities

• A variable relationship between two quantities

• An inverse relationship between two quantities

Which of the following is an example of direct variation?

• Speed and time

• Height and intelligence

• Temperature and color

• Calorie intake and weight gain

In the context of the video, what does a straight line on a graph represent?

• No relationship

• An inverse relationship

• A constant relationship

• A direct variation

How can a curved graph be transformed into a straight line?

• By changing the scale

• By adding more data points

• By using logarithms

• By taking square roots of the values

What is the significance of using square numbers in the video?

• To make the graph more complex

• To change the units of measurement

• To simplify calculations

• To create a straight line graph

What is the purpose of creating a new table with square roots in the video?

• To transform a curved graph into a straight line

• To change the units of measurement

• To simplify the data

• To create a new set of variables

Why are straight lines preferred in graphs for analysis?

• They simplify the process of making predictions.

• They are easier to draw.

• They are more colorful.

• They require less data.

What is the term used for predicting values outside the range of known data?

• Interpolation

• Extrapolation

• Approximation

• Estimation

What is the opposite of extrapolation?

• Approximation

• Calculation

• Interpolation

• Estimation