GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsMedium
A drone is flying in a search pattern. Its path can be described by the linear equation 3x + 2y = 12. A second drone is flying parallel to the first drone. Which of the following equations could represent the path of the second drone?
- Ay = (3/2)x + 5
- By = (2/3)x - 3
- Cy = (-3/2)x + 7
- Dy = (-2/3)x + 1
Show answer & explanationAnswer & explanation
Correct answer: C. y = (-3/2)x + 7
Parallel lines have the same slope. First, convert the given equation to slope-intercept form (y = mx + b) to find its slope. Then, identify the option with the same slope.
Why the other options are wrong
- A. This slope (3/2) is the negative reciprocal of the original slope, indicating a perpendicular line.
- B. This slope (2/3) is incorrect.
- D. This slope (-2/3) is incorrect.
Parallel Lines
Parallel lines are lines in a plane that are always the same distance apart and never intersect. They have the same slope.
- Same slope (m1 = m2)
- Different y-intercepts (b1 ≠ b2)
- Never intersect
- Can be vertical (undefined slope)
Memory trick: Same Slope, Different Stop (y-intercept)!