Question

A straight line PQ passing through points (1,-6) and (6, 14). Determine whether a straight line which passing through (-4,-8) and (-1,7) is parallel to PQ. Explain your answer. [3 markah / marks)​

Answer 1

line not parallel to PQ

Explanation:

Parallel lines have equal slopes

Calculate slopes m of both lines using slope formula

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

with (x₁, y₁ ) = (P (1, - 6) and (x₂, y₂ ) = Q (6, 14 )

`m_(PQ)` =
`(14-(-6))/(6-1)` =
`(14+6)/(5)` =
`(20)/(5)` = 4

Repeat with (x₁, y₁ ) = (- 4, - 8 ) and (x₂, y₂ ) = (- 1, 7 )

m =
`(7-(-8))/(-1-(-4))` =
`(7+8)/(-1+4)` =
`(15)/(3)` = 5

Since slopes are not equal then lines are not parallel