Linear Function Application Game

Linear Function Application Game
This game is a Linear Function Simulator. It challenges you to translate real-world stories into a mathematical equation format called Slope-Intercept Form, specifically using function notation: f(x) = mx + b. Scroll down for a detailed explanation.
 

 

How to Play the Linear Function Application Game

1. Identify the “Starting Value” (b)
   Look for a number in the problem that only happens once. This is your y-intercept.
   Keywords: initial fee, flat fee, start-up, base charge, starts at, starts with.
   Math Role: This is the constant that does not have an x attached to it.
   

2. Identify the “Rate of Change” (m)
   Look for a number that repeats over and over. This is your slope.
   Keywords: per hour, each mile, every day, monthly, yearly.
   Math Role: This is the coefficient that you must multiply by x.
   

3. Determine the Sign (Positive vs. Negative)
   This is the most important part of this specific version of the game:
   Positive (+): If the total is growing. (e.g., adding to a savings account, paying more for more miles).
   Example: f(x) = 20x + 50
   Negative (-): If the total is shrinking or going down. (e.g., a leaking tank, a burning candle, spending money, a draining battery).
   Example: f(x) = -5x + 1004.
   

How to Type Your Answer
The game is strict about the format. You must type the full function:
Begin with f(x)=Follow with your slope and the letter x.
End with your y-intercept.

How to apply Linear Functions?
Linear function applications are real-world scenarios where two variables change at a constant rate relative to one another. In mathematics, these are modeled by the equation f(x) = mx + b.

1. The Initial Value (b)
   This is the starting point. It is a one-time value that doesn’t change regardless of how much time passes.
   Real-world examples: A flat service fee, a security deposit, the height of a plant when you bought it, or the starting balance of a gift card.
   On a Graph: This is the y-intercept.
   

2. The Rate of Change (m)
   This is the slope. It tells you how much the total increases or decreases for every single unit of x.
   Real-world examples: Hourly wages, price per gallon, speed (miles per hour), or the rate at which a battery drains.
   Keywords: Look for “per,” “each,” or “every."
   

Common Application Categories
A. Growth Models (Positive Slope)
These represent totals that increase over time.
Scenario: A fitness center charges a 50 joining fee and 20 per month.
The Math: Since the 50 happens once and the 20 repeats, the equation is f(x) = 20x + 50.

B. Decay or Depletion Models (Negative Slope)
These represent things being used up or decreasing.
Scenario: A 1000-gallon pool is draining at a rate of 50 gallons per hour.
The Math: The start is 1000, and the rate is -50 (because water is leaving).
Equation: f(x) = -50x + 1000 or f(x) = 1000 - 50x.

C. Distance and Travel
Linear functions are the foundation of physics for constant speed.
Scenario: You are 10 miles from home and walking away from it at 3 miles per hour.
Equation: D(t) = 3t + 10, where t is hours and D is distance.

This video gives a clear, step-by-step approach to solve a linear function word problem.

• Show Video

 

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