subhashghosh wrote:

Hi

I did not get why B is the odd man out, please explain.

Regards,

Subhash

This solution could be best explained with a figure;

When do you think the slopes of two lines are equal; either when they are parallel to each other or when they overlap.

Let's consider the case when they coincide:

So; the slopes are equal. "2". and both the lines intercept y-axis at same point. Thus, b=d. With these conditions; all of the

given options but B are possible.

a=m=2

am=-1. Not possible because=2*2=4; not -1

a^2=m^2=2^2=4

|2|=\sqrt{m^2}=\sqrt{2^2}=2am=2*2>0For parallel lines as well; all of the above hold true; because parallel lines have same slope

Let's consider two parallel lines with -ve slope = -3. The only difference in parallel lines and coinciding lines is that they intercept y-axis at different points. Here; we don't care about b or d(y-intercept).

a=m=-3

am=-3*-3=9!=-1

a^2=m^2=(-3)^2=9

|a|=\sqrt{m^2}=3am=-3*-3>0

When the lines are not parallel; their slopes will not be equal. For unequal slopes;

Say a=1; m=2 or anything other than 1.

A. a!=m

B. am!=-1

C. a^2!=m^2

Thus; these options don't hold good for two lines with different slopes.

What if these two lines are perpendicular;

a=-1; m=1

a!=m

am=-1. Possible

a^2=m^2=1. Possible

|1|=\sqrt{m^2}=\sqrt{(-1)^2}=1 Possible

am=-1<0. Not possible.

We see that A and E both aren't true for the perpendicular lines.

Thus; we can conclude that the given equations are equation of parallel lines or overlapping lines, where option B is the odd man out.

_________________

~fluke

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