A line perpendicular to y= 1/4x + 3 passes through the point (0, 6). Which other point lies on the line? Options: A. (4, -2) B. (3, -6) C. (0, -6) D. (-2, 2)

B. (3, -6)

Step-by-step explanation:

Given line

y= 1/4x + 3

given line is in form of y = mx + c

where m is slope of line and c is y intercept

thus, in line  y= 1/4x + 3  m is 1/4 is slope

we know product of slope of two perpendicular line is -1

m1 * m2 = -1

let the line perpendicular to  y= 1/4x + 3 be

y = mx + c

thus

m * 1/4 = -1

m = -4

Thus, in y = mx + c , m is -4

updated equation until now by putting value of m as -4

y = -4x + c

this, line passes through point (0,6)

putting x as 0 and y as 6 in y = -4x + c

we have

6 = -4*0 + c

=> c = 6

Thus, equation of perpendicular line is

y = -4x + 6

we have to find which point from the option lies on y = -4x + 6

lets plug in value of x   from given points and see if value of y calculated  is as given in option . if the value is different then point does not lie on perpendicular line

(4, -2)

y = -4*4 + 6

y = -16 + 6 = -10

-10 is not equal to -2 as given in option, thus point (4,-2 ) does not lie on

y = -4x + 6

(3,-6)

y = -4*3 + 6

y = -12 + 6 = -6

-6 is  equal to -6 as given in option, thus point (3,-6 ) does  lie on

 y = -4x + 6

(0, -6)

y = -4*0 + 6

y = 0 + 6 = 6

6 is not equal to -6 as given in option, thus point (0,-6 ) does not lie on

y = -4x + 6

(-2,2)

y = -4*-2 + 6

y = 8 + 6 = 14

14 is not equal to 2 as given in option, thus point (-2,2 ) does not lie on

y = -4x + 6

Thus, option  B. (3, -6) is the correct choice.