Question

If a ship's path is mapped on a coordinate grid, it follows a straight-line path of slope 4 and passes through point (1, 2).

Part A: What is the equation of the path?

Part B: Does the ship pass through point (7, 24)?

Part C: A second ship follows a straight line, with the equation x + 4y − 20 = 0. Are these two ships sailing perpendicular to each other? Justify your answer.

Answer 1

A.
Using the point-slope form:
y - 2 = 4(x - 1)
y = 4x - 2

B.
We plug the point into the equation to see if it is satisfied:
24 = 4(7) - 2
24 = 26; This is not true so the point is not on the ship's path

C.
The slope of this ship's motion is -1/4, which is the negative reciprocal of the first ship's slope. Therefore, the ships are moving in perpendicular to one another.