GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsMedium
A drone is flying in a search pattern. Its path is recorded on a coordinate plane, and at two specific points, its coordinates are (2, 5) and (8, 17). What is the equation of the line representing the drone's path?
- Ay = 2x + 1
- By = (1/2)x + 4
- Cy = 2x + 5
- Dy = (1/2)x + 5
Show answer & explanationAnswer & explanation
Correct answer: A. y = 2x + 1
First, calculate the slope (m) using the two given points. Then, use the point-slope form (y - y1 = m(x - x1)) or substitute a point and the slope into the slope-intercept form (y = mx + b) to find the y-intercept (b).
Why the other options are wrong
- B. This has an incorrect slope.
- C. This has the correct slope but uses the y-coordinate of the first point as the y-intercept, which is incorrect.
- D. This has an incorrect slope and an incorrect y-intercept.
Equation of a Line from Two Points
To find the equation of a line given two points, first calculate the slope using the slope formula, then use either the point-slope form or substitute a point and the slope into the slope-intercept form to find the y-intercept.
- Slope formula: m = (y2 - y1) / (x2 - x1)
- Point-slope form: y - y1 = m(x - x1)
- Slope-intercept form: y = mx + b
- Any point (x, y) on the line satisfies the equation.
Memory trick: Slope First, Then Point-Slope, or Intercept!