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.

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.

answer

a,b, and d

explanation

a reflection angle is more than

but less than;

an angle that measures

is a reflex angle.(true)

an angle that measures less than

is acute.(true)

provided we are considering angles greater or equal to zero.

an acute angle lies in the range.

an obtuse angle is less than 180° but more than 90°

an angle that measures 300° is obtuse (false)

an angle that measures 65° is an acute angle.(true)