Need expert help - Slope of a line

[voodoo_child]

In the XY-Plane , is the slope of the line k equal to 0 ?

(1) The X- intercept of k is 0

(2) The y-intercept of k is 0.

Logically, OA E makes sense.

However, I need to understand what's wrong with the algebraic method. Please don't reply with an intuitive answer. There is no doubt about OA.

A
Let the equation of line be y=mx+c


1) X intercept => 0=mx+c => x=-c/m; Now if the x-intercept =0; it means that m could be either infinity or a non-zero. I believe that "Infinity/Infinity" is undefined. Hence, m will not be equal to Zero. No. This doesn't make sense. What am I missing here?

2) Y intercept => y= c =0; therefore, y=mx; Not sufficient.

1 and 2) x intercept = 0 and y-intercept = 0=> c=0 and c/m=0 => m is not equal to zero.

It's crazy, but I am a bit lost....

Thoughts?

[Anurag@Gurome]

Hence, m will not be equal to Zero. No. This doesn't make sense. What am I missing here?

If we consider the equation of the line as y = mx + c,
Then from statement 1, we can conclude either of the following,

• 1. c = 0 and m = anything
  • Note that for c = 0, m can be equal to zero. Which is possible when the line is nothing but the X-axis.
  2. c = anything and m = infinity

Hence, slope of the line may or may not be equal to zero.

Taking both statements together, c = 0 and -c/m = 0. As c = 0, -c/m is always equal to zero regardless of the value of m. Hence, m may or may not be equal to zero.

Hence, both statements together are also not sufficient.

The correct answer is E.

[voodoo_child]

• Note that for c = 0, m can be equal to zero. Which is possible when the line is nothing but the X-axis.

Anurag,
thanks for your reply. However, we are given that x-intercept = 0 => c/m = 0. Therefore, if C = 0; how could m equal to 0? 0/0 is an indeterminate form. m CANNOT equal to zero.

X-axis doesn't have an x-intercept = 0. X-intercept on the x-axis could be anything from -infinity to +infinity.


Thoughts?

[GmatMathPro]

1) X intercept => 0=mx+c => x=-c/m; Now if the x-intercept =0; it means that m could be either infinity or a non-zero. I believe that "Infinity/Infinity" is undefined. Hence, m will not be equal to Zero. No. This doesn't make sense. What am I missing here?

The case of m=0 makes nonsense of your equation (x=-c/m) because the very step of going from mx=-c to x=-c/m assumes that m is not equal to 0. That is, dividing both sides of an equation by a quantity is ONLY valid if that quantity is not equal to zero. So your formula for x-intercept, by the nature of its existence, is not equipped to deal with the case m=0 because it is only valid in cases where m is NOT equal to zero.