The answer is

D and C is option are required.the equation of line passing through P is

y-8 = m(x-4)

by using option D

Slope of line = (-1/2)

Because slope of parallel line are equal.

[slope of 4x+8y+12 = 20 is m =(- coefficient of x)/(coefficient of y) = (-4)/8 = -0.5]

=> y-8 =-0.5(x-4)

or 2y+x = 12

By using option c

=> 2y+x = 0


which is only time if x=0 7 y=0

=> y(0,0) lies on line

Rich, Maxpain5, did we get to know if A is an answer? Even I cant figure out how it could be. Experts, any thoughts?

maxpain5 wrote:A Straight line L passes through the point P(4,8).Indicate which of the following options may be required to know if the straight line also passes through any of the points : X(12,16) ,Y(0,0).

A.The line L intersects the straight line M whose equation is 10x + 20y=0
B.The line L passes through the point (2,6)
C.In the equation of the staright line L,the constant term is 0
D.The line L is parallel to the Line Q whose equation is 4x+8y+12=0
E.None of these

Correct Answers are A,B,C,D

My Strategy in solving the above question was to find options that will help in finding the the equation of Line L.
B,C,D options have sufficient data to find the equation of Line L.However,I am not able to understand how can A be used to get equation of line L.

Please help me in the query posted above.

This presentation is more like a GRE Math, Multi Answer Multiple Choice Question, in which more than one answers are always possible.

The question is NOT asking to determine the equation of the line L. It only asks to pick an option that can help us determine that the line L, which already passes through the point P (4, 8), also passes through any of the points X(12, 16) or Y(0, 0).

A. Line M passes through the origin and it intersects line L also. But this information doesn't confirm that line L also passes through the origin or the (12, 16). Hence, this is NOT an option that can help us determine what we are looking for. Eliminate A.

B. If the line L passes through the point (2, 6), then it's slope must be 1, which is same if we take X (12, 16) on line L. Hence, accept B.

C. If the constant term in the equation of a line is zero, then the line must pass through the origin. Hence, accept C.

D. The equation of line Q gives its slope equal to -½, and if line L is parallel to line Q, then the slope of line L must also be equal to -½. None of the two suggested points confirm the slope of line L equal to -½. Eliminate D.

E. Eliminate E.

[spoiler]B and C[/spoiler] are the only options and the shown answers seem wrong.

The answer to this question is correct and A,B,C,D all tell us the required information.

here's how

A.The line L intersects the straight line M whose equation is 10x + 20y=0
equation of line M --> y = (-1/2)x -->(i)
The point of intersection will satisfy both lines M and L
if line L passed through (4,8) and (12, 16 ) then equation of line L -->y = x+4 -->(ii)

lets find the point of intersection of these 2 lines , remember that common point should satisfy both the equations of the line.
So on solving (i)& (ii) we get x= -8/3 and y =4/3 this is the point of interaction and it isn't (12,16) or (0 ,0) so this is not enough.

if line L passed through (4,8) and (0,0 ) then equation of line L -->y = 2x -->(iii)
now again when it interacts with M , the point of interaction will be common for both the lines and hence satisfy both the lines.
so solving (i) and (iii) we get x= 0 and y = 0 hence the point of interaction of both the lines is the origin hence both the lines interact at the origin, so this is sufficient to tell us that line L does pass through the origin.Sufficient.


B.The line L passes through the point (2,6) -
we now know L passes through (4,8) and (2,6 ) so equation of line L ->y = x+ 4
(12, 16 ) satisfies this equation , hence the line L passes through (12, 16). Sufficient

C.In the equation of the staright line L,the constant term is 0
The constant term is the y intercept , given Y intercept is 0 , means when x= 0 then y = 0 so yes the line passes through the origin.Sufficient

D.The line L is parallel to the Line Q whose equation is 4x+8y+12=0
The slope of line Q is (-1/2)so L must have same slope

if line L passed through (4, 8)and ( 0, 0) slope would be 2
if line L passed through (4,8) and (12, 16) slope would be 1

So for line L to have slope (-1/2) it cannot pass through either of these points , hence this option is sufficient too .( The points can be plotted in the Cartesian plane to actually see how this happens).Sufficient.

Correct answer A , B, C, and D all are sufficient.

( When they say does line L pass through ANY of the points (12,16) or (0,0) they mean, does line L pass through any one of the points or both of the points or neither of the points )

My Strategy in solving the above question was to find options that will help in finding the the equation of Line L.
B,C,D options have sufficient data to find the equation of Line L.However,I am not able to understand h


Pass4sure ccie