Writing Linear Equations from Word Problems

The video tutorial explains how to solve linear equations by understanding the slope and Y intercept. It introduces the concept of slope as a unit rate and Y intercept as an initial value. Through an example problem involving boat rental costs, the tutorial demonstrates setting up and solving the equation y = mx + b to determine the number of hours rented and the total cost. The tutorial emphasizes the importance of identifying key terms like 'per' to recognize unit rates and initial fees.

What does the slope in a linear equation typically represent in real-world problems?

• Initial cost before any service

• Total cost after service completion

• Rate of change relating to the cost per unit

• Fixed duration of service

What is the significance of the y-intercept in linear equations?

• It represents the total cost.

• It is the final amount after all calculations.

• It indicates the initial value or starting cost.

• It shows the total time of service.

In the context of renting a boat, what does the initial fee represent?

• The discount offered on the service

• The upfront cost before any usage

• The total cost after returning the boat

• The cost per hour of boat usage

What does the term 'per' indicate in the context of rates?

• A subtraction operation

• An addition operation

• A multiplication operation

• A division operation

What is the unit rate in the context of renting a boat?

• $8 per hour

• $5 per hour

• $12 per hour

• $120 total

How is the y-intercept used in calculating the total cost?

• It is subtracted from the total cost

• It is added to the product of rate and time

• It is multiplied by the number of hours

• It is divided by the number of hours

What does the variable 'x' typically represent in these problems?

• The total cost

• The initial fee

• The rate per unit

• The number of units (e.g., hours or items)

How do you calculate the total hours rented when given a total cost?

• Divide the total cost by the rate

• Subtract the initial fee from the total cost and divide by the rate

• Add the initial fee to the total cost and divide by the rate

• Multiply the rate by total cost

If the boat was rented for 3 hours, how would you calculate the total cost?

• Add the initial fee to the hourly rate and multiply by 3

• Multiply the hourly rate by 3 and add the initial fee

• Divide the initial fee by 3 and subtract from the total cost

• Subtract the hourly rate from the initial fee and multiply by 3

What would be the total cost if the boat was rented for 5 hours?

• $60

• $52

• $40

• $50