In the coordinate plane, Line J passes through the origin as well as

Question

In the coordinate plane, Line J passes through the origin as well as points (a, 2) and (8, a). Which of the following could be the slope of Line J?

A. 1/4
B. 1/2
C. 1
D. 2
E. 4

BrainLab · Accepted Answer

UPDATE 
Slope:  \frac{0-2}{0-a}=2/a   \frac{0-a}{0-8} =a/8 
 \frac{2}{a}=a/8  a=4 -- > Slope=2/a=1/2 Answer (B)

m2k · Answer

Here we know that one of the point is Origin (0,0) and the other two points are (a,2) and (8,a) respectively.
Hence if we calculate and equate the slopes we would get the value of a .
Thus ,
 
m = y2-y1/x2-x1 => a-0/8-0 = 2-0/a-0 which gives us a^2 = 16 . We know slope is +ve because the points lie in the Ist quadrant.
Hence , putting the value of a we would get the slope as m =1/2

The answer is 1/2

thembaseeker · Answer

Equation of line passing through center is given by 
y=mx----(i)
(i) also passes through (a, 2) and (8, a)
therefore 2=ma and a=8m
on solving we get m=1/2

Answer : B

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

That Line J passes through the origin gives you a very helpful bit of information regarding point-slope form (y = mx + b). That tells you that when x = 0, y = 0, meaning that 0 = 0 + b...meaning that b also equals 0. That takes a variable away, allowing you to get to work on the two points knowing that the line has a constant slope, m:

For point (a, 2), that means that 2 = ma.

For point (8, a), that means that a = 8m.

This means that you can plug in a = 8m into the first equation, allowing you to solve for m (the slope):

2 = 8m^2

1/4 = m^2

m = 1/2 (or -1/2).

marvas8581 · Answer

Hi, Kindly let me know if this is a good approach.

Assume a value for 'a'

In this e.g.: (4,2) and (8,4)

Determine the slope as (4-2)/(8-4) = 1/2

Option B?

Bunuel · Answer

The point to note here is that if you plugged -4 for  a  the slope would come up as -1/2. So, algebraic approach, in my opinion, is better for this question.

Nunuboy1994 · Answer

The fact the line J passes through the origin simply means that the y intercept of the equation of line j is 0- more simply, we can just work backwards and plug in values because the slope is the only component of the equation of line j

2= (something) x
 2= 1/2 (4)

4-2 / 8-4 results in the slope so this slope is valid

Thus 
 "B"

bumpbot · Answer

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In the coordinate plane, Line J passes through the origin as well as

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In the coordinate plane, Line J passes through the origin as well as

Prep Toolkit

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