Question

Line b passes through points (6, 7) and (1, 1). Line c passes through points (7, 10) and (2, 4). Are line b and line c parallel or perpendicular?

Answer 1

b and c are parallel lines

Explanation:

Parallel lines have equal slopes

The product of the slopes of perpendicular lines = - 1

Calculate the slopes m of the lines using the slope formula

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

with (x₁, y₁ ) = (6, 7 ) and (x₂, y₂ ) = (1, 1 )

`m_(b)` =
`(1-7)/(1-6)` =
`(-6)/(-5)` =
`(6)/(5)`

Repeat with (x₁, y₁ ) = (7, 10 ) and (x₂, y₂ ) = (2, 4 )

`m_(c)` =
`(4-10)/(2-7)` =
`(-6)/(-5)` =
`(6)/(5)`

Since slope are equal then line b and line c are parallel lines