Exploring Proportional Relationships in Math

This video tutorial covers graphing proportional relationships, interpreting slopes, and comparing proportional relationships using graphs. It includes examples such as the cost of frozen yogurt, weight comparisons between Titan and Earth, and ski lift speeds. The tutorial emphasizes understanding the constant of proportionality and its representation in equations and graphs.

What is the constant of proportionality in the equation y = mx?

• b

• m

• y

• x

Why do all graphs of proportional relationships pass through the origin?

• Because the slope is always zero

• Because the y-intercept is always zero

• Because the x-intercept is always zero

• Because the graph is always a horizontal line

What is the slope of the line represented by the equation y = 0.5x?

• 0

• 1

• 2

• 0.5

If the cost y in dollars for x ounces of frozen yogurt is represented by y = 0.5x, how much does 4 ounces of frozen yogurt cost?

• $2

• $4

• $0.5

• $1

In the context of the frozen yogurt problem, what does the slope represent?

• The total number of ounces

• The total cost of yogurt

• The number of customers

• The cost per ounce of yogurt

What is the equation that represents the weight of an object on Titan if it weighs 105 pounds on Earth and 15 pounds on Titan?

• y = 105x

• y = 15x

• y = 1/7x

• y = 7x

How much would a chunk of ice that weighs 3.5 pounds on Titan weigh on Earth?

• 3.5 pounds

• 24.5 pounds

• 15 pounds

• 21 pounds

What is the slope of the four-person ski lift represented by the equation y = 2.5x?

• 0.5

• 2.5

• 1

• 2

Which ski lift is faster, the four-person lift or the two-person lift?

• Both are the same

• Two-person lift

• Cannot be determined

• Four-person lift

What does the steepness of the graph represent in the context of the ski lift problem?

• The number of people on the lift

• The speed of the lift

• The time taken by the lift

• The distance traveled by the lift