GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsEasy
A pilot is planning a flight path. On a coordinate plane, the aircraft's current position is (3, 5) and its destination is (9, 13). What is the slope of the straight-line path between these two points?
- A2/3
- B4/3
- C3/4
- D3/2
Show answer & explanationAnswer & explanation
Correct answer: B. 4/3
The slope (m) between two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1). For points (3, 5) and (9, 13), the slope is (13 - 5) / (9 - 3) = 8 / 6 = 4/3.
Why the other options are wrong
- A. This would be (6-3)/(13-5) which is incorrect calculation of rise over run.
- C. This would be (9-3)/(13-5) which is calculation of run over rise, then simplified incorrectly.
- D. This would be (9-5)/(13-3) which is an incorrect calculation of rise over run.
Slope of a Line
The slope of a line is a measure of its steepness and direction, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.
- Formula: m = (y2 - y1) / (x2 - x1)
- Positive slope means the line rises from left to right.
- Negative slope means the line falls from left to right.
- Zero slope is a horizontal line; undefined slope is a vertical line.
Memory trick: Slope is 'Rise over Run' – remember the vertical first!