Question

What is the slope and the perpendicular slope on the points given?

Answer 1

-
`(4)/(3)` and
`(3)/(4)`

Explanation:

Calculate the slope m using the slope formula

m =
`\frac{y_{2-y_(1) } }{x_(2)-x_(1) }`

with (x₁, y₁ ) = (- 8, 8) and (x₂, y₂ ) = (4, - 8) ← 2 points on green line

m =
`(-8-8)/(4+8)` =
`(-16)/(12)` = -
`(4)/(3)`

Repeat with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (4, 2) ← 2 points on the blue line

m =
`(2+1)/(4-0)` =
`(3)/(4)`

Since the product of the slopes = -
`(4)/(3)` ×
`(3)/(4)` = - 1

Then the lines are perpendicular

Answer 2

The slopes are:

blue: 4/3 = 1⅓

green: -4/3 = -1⅓

I used rise over run to work these out