Question

3. Determine whether these two lines are parallel, perpendicular, or neither. 1 point

8x + y = 7, 4x + 3y = 12 *
parallel,
perpendicular or
neither

Answer 1

The two lines are neither

Explanation:

• Parallel lines have equal slopes and different y-intercepts

• Perpendicular lines have a product of their slopes = -1

• The slope of a line whose equation is ax + by = c is m =
  `(-a)/(b)`

∵ The equations of the lines are

• 8x + y = 7 ⇒ 1st

• 4x + 3y = 12 ⇒ 2nd

∵ In the 1st equation a = 8 and b = 1

∴ m1 =
`(-8)/(1)` = -8

∴ The slope of the 1st line is -8

∵ In the 2nd equation a = 4 and b = 3

∴ m2 =
`(-4)/(3)`

∴ The slope of the 2nd line is
`(-4)/(3)`

→ By using the facts above

∵ m1 ≠ m2

∴ The two lines are not parallel

∵ m1 × m2 = -8 ×
`(-4)/(3)` =
`(32)/(3)`

∴ m1 × m2 ≠ -1

∴ The two lines are not perpendicular

∴ The two lines are neither parallel nor perpendicular