Question

Line k passes through the point (1, 5) and is perpendicular to the line y = 3x + 1. Which of the following points does line k also pass through?

Select one:
A. (4, 4)
B. (-2, -5)
C. (3, 6)
D. (9, -1)

Answer 1

Option A. (4,4)

Explanation:

step 1

Find the slope of the line k

we know that

If two lines are perpendicular, then the product of their slopes is equal to -1

`m1*m2=-1`

The slope of the given line is
`m1=3`

so

The slope of the line k is

`m2*(3)=-1`

`m2=-(1)/(3)`

step 2

Find the equation of the line k

The equation of the line into point slope form is equal to

`y-y1=m(x-x1)`

we have

`m=-(1)/(3)`

`point(1,5)`

substitute the values

`y-5=-(1)/(3)(x-1)`

step 3

Verify if the line k pass through the given points

Remember that

If the line passes through a point, then the value of x and the value of y of the point must satisfy the equation of the line

Verify each case

case A) (4,4)

`4-5=-(1)/(3)(4-1)`

`-1=-(1)/(3)(3)`

`-1=-1` ----> is true

therefore

The line k pass through the point (4,4)

case B) (-2,-5)

`-5-5=-(1)/(3)(-2-1)`

`-10=-1` -----> is not true

therefore

The line k not pass through the point (-2,-5)

case C) (3,6)

`6-5=-(1)/(3)(3-1)`

`1=-(2)/(3)` -----> is not true

therefore

The line k not pass through the point (3,6)

case D) (9,-1)

`-1-5=-(1)/(3)(9-1)`

`-6=-(8)/(3)` -----> is not true

therefore

The line k not pass through the point (9,-1)