Answer:
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
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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.
