Deja adds $20 to her bus card. Every time she rides the bus, $2 is subtracted from the amount available on her card. After x rides, there are y dollars left on the card. Write a li... Deja adds $20 to her bus card. Every time she rides the bus, $2 is subtracted from the amount available on her card. After x rides, there are y dollars left on the card. Write a linear equation to represent this relationship.
Understand the Problem
The question is asking to create a linear equation that represents the remaining balance on Deja's bus card after a certain number of rides, where a fixed amount is deducted for each ride after an initial amount is added to the card.
Answer
$$ y = 20 - 2x $$
Answer for screen readers
The linear equation representing the relationship is: $$ y = 20 - 2x $$
Steps to Solve
- Identify the Initial Amount
Deja starts with $20 on her bus card. This is the initial amount.
- Determine the Deductions per Ride
For every bus ride, $2 is deducted from the balance. We will represent the number of rides as $x$.
- Set Up the Equation
The remaining balance after $x$ rides can be expressed as: $$ y = 20 - 2x $$ Here, $y$ represents the dollars left on the card after $x$ rides.
The linear equation representing the relationship is: $$ y = 20 - 2x $$
More Information
This equation shows that Deja starts with $20 and loses $2 with each bus ride. Thus, the amount left on her card decreases linearly with the number of rides taken.
Tips
- Forgetting to include the initial amount of $20.
- Miscalculating the deduction amount per ride. It's crucial to know that it's $2 per ride.
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