Direct Proportionality and Graph Interpretation

The video explains the concept of direct proportion, where two variables increase or decrease at the same rate. It uses the example of hours worked and pay to illustrate this relationship. The video also demonstrates how to graph direct proportion relationships, highlighting that the graph is a straight line passing through the origin. It shows how to use such graphs to calculate earnings for different hours worked. The video concludes by summarizing the key points about direct proportion and its graphical representation.

What does it mean when two variables are directly proportional?

• One variable increases while the other decreases.

• Both variables increase at the same rate.

• Both variables decrease at different rates.

• One variable remains constant while the other changes.

In the example of hours worked and money earned, what does the proportional symbol indicate?

• The variables are inversely proportional.

• The variables are directly proportional.

• The variables are unrelated.

• The variables are constant.

If you work 5 hours and earn 60 pounds, how much would you earn for 10 hours?

• 80 pounds

• 60 pounds

• 100 pounds

• 120 pounds

What is a key feature of a graph representing direct proportionality?

• It is a horizontal line.

• It has multiple peaks.

• It passes through the origin.

• It is a curved line.

On a graph of direct proportionality, what does the point (0,0) represent?

• The point where the line ends.

• The point where both variables are zero.

• The starting point of the variables.

• The maximum value of the variables.

How can you determine earnings for a specific number of hours using a graph?

• By drawing a diagonal line from the origin.

• By drawing a line parallel to the y-axis.

• By drawing a vertical line from the x-axis.

• By drawing a horizontal line from the x-axis.

If you worked 3.5 hours, how much would you earn according to the graph?

• 30 pounds

• 42 pounds

• 35 pounds

• 50 pounds

What happens to one variable if the other variable doubles in a direct proportionality?

• It remains the same.

• It triples.

• It doubles.

• It halves.

What is the main takeaway about the relationship between directly proportional variables?

• They increase or decrease at different rates.

• They increase or decrease proportionally.

• They are inversely related.

• They remain constant.

How does the graph of directly proportional variables always appear?

• As a curved line.

• As a straight line through the origin.

• As a horizontal line.

• As a vertical line.