Math Problem Statement

Juan makes $20 an hour at his job. He creates an equation to predict how much money he will make based on how many hours he works. Determine which function type best models this scenario.

Solution

To solve this question, let's analyze the scenario:

Juan earns $20 per hour at his job. The problem asks for the best type of function to model how much he will make based on the number of hours he works.

  • Since his earnings increase by a constant rate of $20 for each additional hour he works, this relationship between hours worked and total earnings is linear.
  • A linear function has the form y=mx+by = mx + b, where mm is the constant rate of change (in this case, $20 per hour) and bb is the starting amount (which is $0 if he starts with no money earned initially).

So, the correct answer is:

  • A linear function

Let me know if you want further details or have questions.

Here are 5 additional related questions:

  1. How would the function change if Juan’s hourly wage increased over time?
  2. What would the equation look like if Juan had a starting bonus of $50?
  3. How would you model Juan’s earnings if his pay rate doubled every hour?
  4. How can you determine if a real-life scenario fits a linear function?
  5. What does the slope of a linear function represent in practical terms?

Tip: In general, if the change in a quantity is constant over time, a linear function is often the best model.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Functions

Formulas

y = mx + b

Theorems

Slope-intercept form of a linear equation

Suitable Grade Level

Grades 8-10