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

Answer:

$y=\dfrac{4}{3}x-8$

Option 3 is correct

Step-by-step 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: $y=-\dfrac{3}{4}x+8$

Put x=6, y=0

$0=-\dfrac{3}{4}\cdot 6+8$

$0\neq\dfrac{7}{2}$

False

Option 2: $y=-\dfrac{3}{4}x+6$

Put x=6, y=0

$0=-\dfrac{3}{4}\cdot 6+6$

$0\neq\dfrac{3}{2}$

False

Option 3: $y=\dfrac{4}{3}x-8$

Put x=6, y=0

$0=\dfrac{4}{3}\cdot 6-8$

$0=0$

True

Option 1: $y=\dfrac{4}{3}x-6$

Put x=6, y=0

$0=\dfrac{4}{3}\cdot 6-6$

$0\neq2$

False

Hence, The perpendicular equation is $y=\dfrac{4}{3}x-8$