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 one point, it is at (2, 5) and later at (8, 17). Which of the following equations represents the line of the drone's path between these two points?
- Ay = 2x + 1
- By = 2x + 5
- Cy = 3x + 2
- Dy = 3x - 1
Show answer & explanationAnswer & explanation
Correct answer: A. y = 2x + 1
First, calculate the slope (m) using the two points: m = (y₂ - y₁) / (x₂ - x₁). Then, use the point-slope form (y - y₁ = m(x - x₁)) or slope-intercept form (y = mx + b) with one of the points and the calculated slope to find the y-intercept (b) and the equation of the line.
Why the other options are wrong
- B. This equation has the correct slope but an incorrect y-intercept.
- C. This equation has an incorrect slope and y-intercept.
- D. This equation has an incorrect slope.
Equation of a Line from Two Points
To find the equation of a line given two points, first calculate the slope (m), then use the point-slope form (y - y₁ = m(x - x₁)) or slope-intercept form (y = mx + b) to determine the y-intercept (b) and write the final equation.
- Slope formula: m = (y₂ - y₁) / (x₂ - x₁).
- Point-slope form: y - y₁ = m(x - x₁).
- Slope-intercept form: y = mx + b.
Memory trick: Two 'P'oints 'P'romise a 'P'erfect 'P'ath.