GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsEasy
A biologist is studying the growth of a plant. She records the plant's height in centimeters (h) over time in weeks (t). The relationship is modeled by the equation h(t) = 3t + 5. What does the number 3 represent in this equation?
- AThe initial height of the plant.
- BThe number of weeks the plant has been growing.
- CThe total height of the plant after t weeks.
- DThe growth rate of the plant per week.
Show answer & explanationAnswer & explanation
Correct answer: D. The growth rate of the plant per week.
In a linear equation of the form y = mx + b, 'm' represents the slope, which indicates the rate of change. Here, 3 is the coefficient of 't', representing the plant's growth in centimeters per week.
Why the other options are wrong
- A. The initial height is represented by the y-intercept, which is 5 in this equation.
- B. The number of weeks is represented by the variable 't', not the coefficient 3.
- C. The total height is represented by h(t), the entire output of the function.
Slope as Rate of Change
The slope of a linear equation describes the rate at which the dependent variable changes for every unit increase in the independent variable.
- Represented by 'm' in y = mx + b.
- Indicates how fast or slow a quantity is changing.
- Units of slope are 'units of y per unit of x'.
Memory trick: My equation's slope is the rate, my intercept the start.