Question

Line 1: (7,3) and (8,7)

Line 2: (-5,-4) and (-1,-5)
What is the slope, and is it parallel, perpendicular, or neither?

Answer 1

lines are perpendicular

Explanation:

Parallel lines have equal slopes

The product of the slopes of perpendicular lines = - 1

Calculate the slopes m of the 2 lines using the slope formula

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

with (x₁, y₁ ) = (7, 3 ) and (x₂, y₂ ) = (8, 7 )

m =
`(7-3)/(8-7)` =
`(4)/(1)` = 4

Repeat with

(x₁, y₁ ) = (- 5, - 4 ) and (x₂, y₂ ) = (- 1, - 5 )

m =
`(-5-(-4))/(-1-(-5))` =
`(-5+4)/(-1+5)` =
`(-1)/(4)` = -
`(1)/(4)`

Slopes are not equal so lines are not parallel

4 × -
`(1)/(4)` = - 1

Then the 2 lines are perpendicular to each other