What describes the relation ship between.....& find the slope please!!!!! Quick questions?

Question

Find the slpe of a ladder placed 4ft from the wall and touching the wall at 12ft


&

What describes the relation ship between
6x - 2y =1 and line x + 3y =12
parallel perpendicular skew or equivalent

Answer 1

PROBLEM 1:

Slope is defined as the "rise" over the "run". For the ladder, the rise (height) is 12 ft. and the run is 4 ft.

12 / 4 = 3

So the slope is 3.

PROBLEM 2:

Write each equation is slope intercept form (y = mx + b)

Eq. 1:
6x - 2y = 1
-2y = -6x + 1
y = 3x - 1/2
Slope is 3.

Eq. 2:
x + 3y = 12
3y = -x + 12
y = (-1/3)x + 4
Slope is -1/3.

Parallel lines have the same slope, so these lines aren't parallel.

Perpendicular lines have slopes that are negative reciprocals.
3 and -1/3 *are* negative reciprocals, so these lines are perpendicular.

(Skew lines would be if neither of the prior conditions applied).

The answer is they are *perpendicular*