GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsHard
A drone is flying in a search pattern. Its path is recorded on a coordinate plane, and at one point, it is at (2, 7). Later, it is at (8, 19). Which of the following is the equation of the line representing the drone's path between these two points?
- Ay = (1/2)x + 6
- By = (1/3)x + 2
- Cy = 3x + 1
- Dy = 2x + 3
Show answer & explanationAnswer & explanation
Correct answer: D. y = 2x + 3
First, find the slope (m) using m = (y2 - y1) / (x2 - x1) = (19 - 7) / (8 - 2) = 12 / 6 = 2. Then, use the point-slope form y - y1 = m(x - x1) with one of the points, say (2, 7): y - 7 = 2(x - 2). Simplify to y - 7 = 2x - 4, which gives y = 2x + 3. Alternatively, use y = mx + b and substitute a point and the slope to find b: 7 = 2(2) + b => 7 = 4 + b => b = 3.
Why the other options are wrong
- A. The slope is incorrect, and the y-intercept is also incorrect.
- B. The slope is incorrect, and the y-intercept is also incorrect.
- C. The slope is incorrect (3 instead of 2).
Equation of a Line from Two Points
To find the equation of a line given two points, first calculate the slope (m), then use either the point-slope form (y - y1 = m(x - x1)) or the slope-intercept form (y = mx + b) to find the y-intercept (b).
- Slope formula: m = (y2 - y1) / (x2 - x1).
- Point-slope form is useful for direct substitution.
- Slope-intercept form (y = mx + b) is the most common final form.
- Verify the equation by substituting both original points.
Memory trick: Two points 'P'ave the way to 'M'aking the 'B'est line!