The graph of which of the following equations is a straight line that is parallel to line l in the figure above?

(A) 3y − 2x = 0
(B) 3y + 2x = 0
(C) 3y + 2x = 6
(D) 2y − 3x = 6
(E) 2y + 3x = −6

Kudos for a correct solution.


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the slope of the given line is +ve. so you need another +ve slope line to be parallel to it. Only options A and D have that. Out of which only option a matches with the slope of 2/3 of line l. so A.

I'll go with A.
For the lines to be parallel, the slope must be the same
for the perpendicular lines, the slope of the second line is the negative reciprocal of the slope of the first line. Here, we are looking for a line with the same slope as the drawn line - 2/3
only A has the same slope.

Clearly, the line passes through (0,2) and (-3,0). The slope for this line : 2/3.
A line parallel to this line will have the same slope.
So, option(A) is having the slope as 2/3.

Answer is A

It is necessary to rule out B,C,E for their slopes are <0

Either you actually calculate the slope to rule out B,C,E or just look at the positive nature and rule these 3 options out.

Another way to look at slope can be to interpret it visually by noticing the transition through its two points (intercepts): when y increased by 2 (from 0 to 2), x increased by 3 (from -3 to 0), therefore slope = 2/3.

Attached is a visual that should help.

From the figure given, we can write the equation of the line l as -

\(\frac{y}{2} +\frac{x}{-3} = 1\)
\(3y - 2z = 6\)

Now any line which is parallel to the above line can be written as 3y - 2z = k where k is any real number.

Therefore we just need to look at the answer options and find an equation which matches the above general form.

And there is only one option 3y - 2z = 0. Hence the correct answer option is A.


Thanks,
Saquib
Quant Expert
e-GMAT

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Recall that if two lines are parallel, then they have the same slope. Therefore, to solve this problem, we need to find the slope of the given line first. Using the provided diagram, we see that we have points of (-3,0) and (0,2). So we have a slope of:

(change in y)/(change in x) = (0 - 2)/(-3 - 0) = -2/-3 = 2/3

We also see that the y intercept is 2; thus, the equation of line l is:

y = (2/3)x + 2

We can manipulate the equation for line l to look more like the answer choices. We can start by multiplying the entire equation by 3 and we obtain:

3y = 2x + 6

3y - 2x = 6

Since answer choice A is the only answer with “3y - 2x,” we see that 3y - 2x = 0, must be parallel to line l.

Answer: A
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Rule 1 - Parallel lines have the same slope.
Rule 2 - If y increases, as x increases then slope is always positive => It means option B,C and E out due to negative slope
slope of line -> y intercept/x intercept => 2/3
so answer is A