Question

What is the original slope and what is the perpendicular slope?

Answer 1

- 2 and
`(1)/(2)`

Explanation:

Calculate the slope m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (- 3, 5) and (x₂, y₂ ) = (0, - 1) ← 2 points on the green line

m =
`(-1-5)/(0+3)` =
`(-6)/(3)` = - 2

Repeat with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (6, 0) ← 2 points on the blue line

m =
`(0+3)/(6-0)` =
`(3)/(6)` =
`(1)/(2)`

Since the product of the slopes = - 2 ×
`(1)/(2)` = - 1

Then the lines are perpendicular

Answer 2

green line:

rise= -6

run= 3

rise/run = slope

therofore the slope = -6/3 = -2

blue line:

rise=3

run=6

rise/run = slope

therofore the slope = 3/6 = 1/2