GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsEasy
A production manager is analyzing the relationship between the number of units produced, x, and the total production cost, C(x). The manager models this relationship with the linear equation C(x) = 15x + 500. What does the number 15 represent in this equation?
- AThe maximum number of units that can be produced.
- BThe cost to produce each additional unit.
- CThe fixed cost of production, regardless of units produced.
- DThe total production cost for 500 units.
Show answer & explanationAnswer & explanation
Correct answer: B. The cost to produce each additional unit.
In a linear equation of the form y = mx + b, 'm' represents the slope, which indicates the rate of change. Here, 15 is 'm', showing the cost per unit.
Why the other options are wrong
- A. This is incorrect; the equation does not provide information about production capacity.
- C. This is incorrect; the fixed cost is represented by the y-intercept, which is 500 in this equation.
- D. This is incorrect; 15 is the cost per unit, not a total cost for a specific number of units.
Slope in Linear Equations
The slope (m) in a linear equation y = mx + b represents the rate of change of the dependent variable (y) with respect to the independent variable (x).
- Indicates how much 'y' changes for each unit change in 'x'.
- Can be positive (increasing), negative (decreasing), zero (constant), or undefined (vertical line).
- Often interpreted as a 'rate' in real-world scenarios.
Memory trick: Y-intercept is your START, Slope is your RATE.