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 (cm) over several weeks. The data points are plotted on a coordinate plane, where the x-axis represents the number of weeks and the y-axis represents the height in centimeters. If the biologist observes that the plant's height increases by 2.5 cm every week, what is the slope of the line representing this growth?
- A2.5
- B0.4
- C5.0
- D1.0
Show answer & explanationAnswer & explanation
Correct answer: A. 2.5
The slope of a line represents the rate of change. In this scenario, the plant's height increases by 2.5 cm for every 1 week that passes. This directly corresponds to the definition of slope as 'rise over run'.
Why the other options are wrong
- B. This would be the slope if the plant grew 1 cm every 2.5 weeks, which is incorrect.
- C. This would indicate a growth of 5 cm per week, which is double the stated rate.
- D. This would indicate a growth of 1 cm per week, not 2.5 cm per week.
Slope as Rate of Change
Slope quantifies how much the dependent variable (y) changes for every unit change in the independent variable (x), representing a rate.
- Slope = Δy / Δx (rise over run)
- Positive slope means y increases as x increases
- Negative slope means y decreases as x increases
Memory trick: Rise Up, Run Across – Slope's the Rate!