The point nearest to the origin on a line is at (4, -4). find the standard form of the equation of the line.

Choice C) x-y-8 = 0

How to get this

First find the equation of the line through the origin (0,0) and (4,-4)

slope:

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

m = (-4-0)/(4-0)

m = -4/4

m = -1

Slope intercept form:

y = mx+b

y = -1*x+b

-4 = -1*4+b

-4 = -4+b

-4+4 = -4+b+4

0 = b

b = 0

The equation of the line through (0,0) and (4,-4) is y = -1x+0 which simplifies to y = -x

The perpendicular line is the one we want. This line will go through (4,-4)

The original slope is m = -1 = -1/1

The perpendicular slope is -1/m = -1/(-1/1) = 1

Recompute the y intercept

y = mx+b

-4 = 1*4+b

-4 = 4+b

-4-4 = 4+b-4

-8 = b

b = -8

The slope intercept equation we want is

y = x-8

Convert to standard form

y = x-8

y-y = x-8-y

0 = x-y-8

x-y-8 = 0

Which is why the answer is choice C

The line x-y-8=0 contains the point (4,-4) which is the closest point to the origin.

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step-by-step explanation:

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