If a ship's path is mapped on a coordinate grid, it follows a straight-line path of slope 5 and passes through point (2, 3)
part a: what is the equation of the path?
part b: does the ship pass through point (6, 25)?
part c: a second ship follows a straight line, with the equation x + 5y − 15 = 0. are these two ships sailing perpendicular to each other? justify your answer.

Part A.

Call m the slope

Equation:

y -yo = m( x- xo)

y - 3 = 5 (x - 2)

y = 5x - 10 + 3

y = 5x - 7

Part B.

Check if point (6, 25) belongs to the equation found above

y = 5(6) - 7 = 30 - 7 = 23

Given that 23 ≠ 25 the ship does not pass through point (6,25)

Part C.

The equation of the path of the second ship can be written as:

y = - x/5 + 3

The slope is the coefficient of x, this is - 1/5.

Then this slope is the slope of the first ship multiplied by - 1 and inverted. This is the condition to be parallel lines. So, indeed the two ships are sailing perpendicular to each other.