Slope, Rates, and Proportionality

The video tutorial covers the concept of proportional relationships, focusing on unit rates and constants of proportionality. It explains how to graph these relationships and interpret the slope as a unit rate. Examples include calculating distances traveled by a car and analyzing mowing rates. The tutorial also compares different proportional relationships, such as coffee shop prices and bolt inspection rates at companies, using slope calculations to determine cost and efficiency differences.

What is the constant of proportionality if a car travels 55 miles in one hour?

• 0

• 110

• 55

• 1

In the equation y = mx, what does 'm' represent?

• The y-intercept

• The constant of proportionality

• The slope

• The x-coordinate

If Polly mows 35 square feet in 2.5 minutes, what is her unit rate in square feet per minute?

• 35

• 2.5

• 14

• 28

How many square feet will Polly have mowed after 3 minutes if her unit rate is 14 square feet per minute?

• 28

• 42

• 56

• 14

What is the slope of a line if the rise is 28 and the run is 2?

• 56

• 2

• 28

• 14

Which coffee shop is more expensive if Shop A charges $2.75 per cup and Shop B charges $2.50 per cup?

• Shop A

• Shop B

• Both are the same

• Cannot be determined

If Shop A sells 10 cups of coffee at $2.75 each, what is the total cost?

• $27.50

• $25.00

• $30.00

• $20.00

How many bolts per minute does Company X inspect if they inspect 5000 bolts in 40 minutes?

• 125

• 200

• 100

• 150

What is the difference in the number of bolts inspected by Company X and Company Y after 64 minutes if Company X inspects 125 bolts per minute and Company Y inspects 123 bolts per minute?

• 64

• 0

• 128

• 256

Which company inspects more bolts per minute if Company X inspects 125 bolts per minute and Company Y inspects 123 bolts per minute?

• Both inspect the same

• Company X

• Company Y

• Cannot be determined