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

Answer:

Option A. (4,4)

Step-by-step 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

$m2*(3)=-1$

$m2=-\frac{1}{3}$

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

$m=-\frac{1}{3}$

$point(1,5)$

substitute the values

$y-5=-\frac{1}{3}(x-1)$

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)

$4-5=-\frac{1}{3}(4-1)$

$-1=-\frac{1}{3}(3)$

$-1=-1$ ----> is true

therefore

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

case B) (-2,-5)

$-5-5=-\frac{1}{3}(-2-1)$

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

therefore

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

case C) (3,6)

$6-5=-\frac{1}{3}(3-1)$

$1=-\frac{2}{3}$ -----> is not true

therefore

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

case D) (9,-1)

$-1-5=-\frac{1}{3}(9-1)$

$-6=-\frac{8}{3}$ -----> is not true

therefore

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