Unit Rates and Proportional Relationships

This video tutorial explains how to write an equation to express the proportional relationship between distance and time by finding the unit rate. It covers the concept of unit rate, how to calculate it, and how to use it to write proportional equations. The tutorial also addresses common confusions, such as whether to divide distance by time or vice versa, and provides guidance on dividing decimals. Additionally, it demonstrates how to use graphs to find the constant of proportionality and concludes with the final equation representing the relationship.

What is the purpose of writing an equation to express a proportional relationship?

• To find the total distance traveled

• To express the relationship between two variables

• To calculate the average speed

• To determine the time taken for a journey

How do you calculate the unit rate?

• By multiplying distance and time

• By dividing distance by time

• By adding distance and time

• By dividing time by distance

If you travel 150 miles in 2 hours, what is your unit rate?

• 75 miles per hour

• 150 miles per hour

• 2 miles per hour

• 300 miles per hour

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

• The total distance

• The constant of proportionality

• The independent variable

• The dependent variable

What is a common mistake students make when calculating unit rates?

• Adding distance and time

• Multiplying distance by time

• Dividing time by distance

• Subtracting time from distance

Why do we multiply by a power of 10 when dividing decimals?

• To decrease the quotient

• To increase the dividend

• To simplify the equation

• To make the divisor a whole number

What is the result of dividing 900 by 225?

• 2

• 3

• 4

• 5

What does a straight line through the origin on a graph indicate?

• The relationship is not proportional

• The ratio of variables is constant

• The variables are independent

• The variables are dependent

What is the unit rate if the ratio of miles to hours is constant at 3?

• 2 miles per hour

• 4 miles per hour

• 1 mile per hour

• 3 miles per hour

What is the equation relating distance (d) and time (t) if the unit rate is 3?

• d = 3 + t

• d = 3t

• d = t - 3

• d = t/3