Question

What is the equation of the line that is perpendicular to the given line and has an x-intercept of 6?

y = –Three-fourthsx + 8

y = –Three-fourthsx + 6

y = Four-thirdsx – 8

y = Four-thirdsx – 6

Answer 1

Correct Answer: C. y = Four-thirdsx – 8

Answer 2

`y=(4)/(3)x-8`

Option 3 is correct

Explanation:

To find: The equation of perpendicular to given line and has x-intercept 6

x-intercept is on x-axis where y value is 0.

Therefore, x-intercept: (6,0)

Now we will check each point for each option.

Option 1:
`y=-(3)/(4)x+8`

Put x=6, y=0

`0=-(3)/(4)\cdot 6+8`

`0\\eq(7)/(2)`

False

Option 2:
`y=-(3)/(4)x+6`

Put x=6, y=0

`0=-(3)/(4)\cdot 6+6`

`0\\eq(3)/(2)`

False

Option 3:
`y=(4)/(3)x-8`

Put x=6, y=0

`0=(4)/(3)\cdot 6-8`

`0=0`

True

Option 1:
`y=(4)/(3)x-6`

Put x=6, y=0

`0=(4)/(3)\cdot 6-6`

`0\\eq2`

False

Hence, The perpendicular equation is
`y=(4)/(3)x-8`