The equation 2x+ky=-k is the equation of a line. In each of the parts below, det

Question

The equation 2x+ky=-k is the equation of a line. In each of the parts below, determine which values of the constant k, if any, will allow the line to have the property listed in that part.
A. The line is horizontal B. The line is vertical C. The line passes within 1 unit of the origin The equation 2x+ky=-k is the equation of a line. In each of the parts below, determine which values of the constant k, if any, will allow the line to have the property listed in that part.
A. The line is horizontal B. The line is vertical C. The line passes within 1 unit of the origin
A. The line is horizontal B. The line is vertical C. The line passes within 1 unit of the origin

Explanation / Answer

2x+ky=-k

ky=-2x-k

y=(-2/k)x -1

slope is (-2/k), y intercept (0,-1)

A. The line is horizontal when slope =0

-2/k=0

never happens

B. The line is vertical when slope tends to infinity

it happens when k=0

equation of line is 2x+0=0 =>x=0, y axis

C) The line passes within 1 unit of the origin

y=(-2/k)x -1

y intercept is (0,-1) which is unit from origin

lines passes through with in 1 unit from origin for all value of k ,

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