Comparing Costs with Linear Equations

The video tutorial explains how to compare rental costs from two companies using linear equations. Company A charges a $20 flat fee plus 20 cents per mile, while Company B charges $35 plus 15 cents per mile. The tutorial guides students through setting up and solving a word equation to find the number of miles at which the costs are equal. It emphasizes understanding linear equations, identifying rates and initial conditions, and solving for variables. The video concludes with a summary and encourages viewers to subscribe for more tutorials.

What is the initial cost to rent a car from Company A?

• 20 cents per mile

• $20

• $35

• 15 cents per mile

How much does Company B charge per mile?

• 25 cents

• 10 cents

• 15 cents

• 20 cents

What is the initial fee charged by Company B?

• 15 cents per mile

• 20 cents per mile

• $35

• $20

What is the rate per mile charged by Company A?

• 20 cents

• 15 cents

• 25 cents

• 10 cents

What is the purpose of setting up a word equation in this problem?

• To calculate the total cost

• To determine the cheaper company

• To compare the initial fees

• To find the point where costs are equal

In the context of linear equations, what does 'm' represent?

• The initial cost

• The rate per mile

• The total distance

• The final cost

What does 'b' represent in the equation y = mx + b?

• The total cost

• The initial condition

• The rate per mile

• The slope

Why is Company A cheaper if you drive fewer miles?

• Higher rate per mile

• Higher initial cost

• Lower rate per mile

• Lower initial cost

What is the significance of the 'b' value in the context of this problem?

• It represents the slope

• It is the rate per mile

• It is the initial cost

• It is the total cost

What is the first step in solving the equation for equal costs?

• Divide by the total miles

• Add the rates per mile

• Subtract the initial costs

• Subtract 0.15m from both sides