Question

Determine if the two lines are perpendicular. Explain how you know by calculating the slopes and comparing the slopes in 2-3 sentences.

Answer 1

The two lines are not perpendicular because the product of their slopes is not equal to -1

Explanation:

The product of the slopes of the perpendicular line is -1

• That means one of them is and additive and multiplicative inverse of the other

• If the slope of one of them is m, then reciprocal m and change its sign, then the slope of the perpendicular is
  `-(1)/(m)`
• The formula of the slope is
  `m=(y_(2)-y_(1))/(x_(2)-x_(1))`

Let us find from the graph two points lie on each line and calculate the slopes of them and then find its product if the product is -1, then the two lines are perpendicular

From the graph

∵ The red line passes through points (4 , 0) and (0 , 8)

∴
`x_(1)` = 4 and
`x_(2)` = 0

∴
`y_(1)` = 0 and
`y_(2)` = 8

∵
`m=(8-0)/(0-4)=(8)/(-4)=-2`

∴ The slope of the red line is -2

∵ The blue line passes through points (5 , 5) and (0 , -5)

∴
`x_(1)` = 5 and
`x_(2)` = 0

∴
`y_(1)` = 5 and
`y_(2)` = -5

∵
`m=(-5-5)/(0-5)=(-10)/(-5)=2`

∴ The slope of the blue line is 2

∵ The products of the slopes of the two lines = -2 × 2 = -4

∴ The product of the slopes of the lines not equal -1

∴ The two lines are not perpendicular