GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsEasy
A scientist is tracking the growth of a bacterial colony. The graph shows the number of bacteria, N, over time, t, in hours. If the graph is a straight line passing through (0, 100) and (4, 700), what is the slope of the line, representing the average growth rate of the colony?
- A600 bacteria/hour
- B150 bacteria/hour
- C200 bacteria/hour
- D100 bacteria/hour
Show answer & explanationAnswer & explanation
Correct answer: B. 150 bacteria/hour
The slope of a line is calculated using the formula (y2 - y1) / (x2 - x1). Given the points (0, 100) and (4, 700), the slope is (700 - 100) / (4 - 0) = 600 / 4 = 150.
Why the other options are wrong
- A. This is the total change in bacteria, not the rate of change (slope).
- C. This would be the result if the change in x was 3 instead of 4.
- D. This is the y-intercept, not the slope.
Slope of a Line
The slope of a line measures its steepness and direction. It is the ratio of the vertical change (rise) to the horizontal change (run) between any two distinct points on the line.
- Formula: m = (y2 - y1) / (x2 - x1).
- Positive slope means the line goes up from left to right.
- Negative slope means the line goes down from left to right.
- Zero slope is a horizontal line; undefined slope is a vertical line.
Memory trick: Rise over run, like climbing a hill!