Hiker Distance and Rate Problems

The video tutorial discusses interpreting proportional relationship graphs, focusing on the equation y = kx. It explains how to find unit rates from graphs, write equations for proportional relationships, and apply these concepts to real-world scenarios. The tutorial uses a graph of two hikers to demonstrate calculating unit rates, writing equations, and determining distances traveled over time. It concludes by comparing the hikers' paces and explaining how to identify faster paces using graph steepness and unit rates.

What is the general form of a proportional relationship equation?

• y = x^2

• y = k/x

• y = kx

• y = mx + b

In the given scenario, what does the y-axis represent?

• Speed in miles per hour

• Distance in miles

• Number of hikers

• Time in hours

How is the unit rate defined in the context of the hikers' graph?

• Miles per gallon

• Miles per hour

• Gallons per mile

• Hours per mile

What is the unit rate for the blue hiker?

• 3 miles per hour

• 2 miles per hour

• 1 mile per hour

• 0.5 miles per hour

What is the unit rate for the orange hiker?

• 1 mile per hour

• 3 miles per hour

• 0.5 miles per hour

• 2 miles per hour

What equation represents the distance traveled by the blue hiker?

• y = 0.5x

• y = 3x

• y = 2x

• y = x + 2

How can you verify the equation for the blue hiker using the graph?

• By ensuring the line is horizontal

• By confirming the line is vertical

• By checking if the line passes through the origin

• By checking if the line is a parabola

How far does the blue hiker travel in 15 hours?

• 60 miles

• 15 miles

• 30 miles

• 45 miles

Which hiker has a faster pace?

• Both have the same pace

• Pace cannot be determined

• The orange hiker

• The blue hiker

What does a steeper line on the graph indicate about a hiker's pace?

• Slower pace

• Faster pace

• Variable pace

• Constant pace