Question #0519e

1 Answer
Mar 8, 2017

You need more information to assign a value to #k# so is the wording of this question complete and/or correct?

Explanation:

NOTE THAT you are allowed to call a straight line graph a curve.

Consider the standardised form of #y=mx+c#

Now consider the given curve #y=k/1-2x#

#k/1# is the same as just #k# giving:

#y=k-2x#

Put this in the same order as the standardised form and we have

#color(red)(y=-2x+k) larr" This is the equation of a strait line!"#

We are told that the tangent has the gradient of -2 which matches the -2 in #y=-2x+k#

So the tangent is parallel to the line. The very fact it is a tangent (to a straight line plot) means that it coincides with the line.

Thus any point (x,y) will be on both the original line and its tangent.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Set #x=2#

#y=-2x+k#

#y=-2(2)+k#

#y=-4+k#

So #" " k=y+4 #

In other words you need to know a value for #y# to determine the value of #k#

A state where you can not get an answer is called 'indeterminate'.