Ndicate the equation of the line that is the perpendicular bisector of the segment with endpoints (4, 1) and (2, -5).

A line that is perpendicular to another line has a slope that is the opposite reciprocal of the slope of the line it is perpendicular to.

First, we need to find the slope of the line.

slope(m) = y2-y1 / x2-x1

m = -5 - 1 / 2 - 4

m = -6 / -2

m = 3 (neg / neg = pos)

Next, we need to find the y intercept.

To find the y intercept, we plug in what we know into the slope-intercept equation

y=mx+b

y=3x+b (Now we pick one of the coordinates to plug in)

1 = 3(4) + b

1= 12 + b

-12 -12

-11 = b

The y intercept is (0,-11)

The equation of the line is y=3x-11

Remember that the slope of a perpendicular line is the opposite reciprocal of the slope of the line it is perpendicular to

The slope of the perpendicular line is -1/3

The equation of the perpendicular line is

y=-1/3x-11

third option: 6x+8

step-by-step explanation:

we can see that the given question is a sum of series and the values of n vary from 0 to 3

the first term will be:

when n=0, [(0)*x+2] => (0+2) => 2

when n=1, [(1)*x+2] => (x+2) => x+2

when n=2, [(2)*x+2] => 2x+2

when n=4, [(3)*x+2] => 3x+2

so adding up all the terms will give us:

=2+x+2+2x+2+3x+2

=x+2x+3x+2+2+2+2

=6x+8

so,

third option is the correct answer ..