The graph of which of the following equations is a straight line that

A line is parallel to line l if it has the same value for m in the formula y=mx+b. So we have to calculate the value of m of the line l in the picture:

y2-y1/x2-x1 = 2-0 / 0-(-3) = 2/3 =m = slope of line l

If you rewrite (A) to y = 2/3x, you see that A has the same slope.

Answer A.

Observation 1: Line is upward rising so SLOPE MUST BE POSITIVE

Observation 2: Y-Intercept is +2

Observation 3: Slope = 2(y-intercept) / 3(x-interecpt) = 2/3

Based on "Observation 1" Options B, C and E are ruled out

Now, Options A and D remain

Based on Observation 3, Option D is ruled out which has slope=3/2

Answer: Option A

P.S. Observation 2 in this question was not necessary as we had to find a line parallel to given line for which Y-Intercept must be different. But these are critical and Primary observations that one must make before starting to solve in question of Co-ordinate Geometry

hi,
even observation 1 is not necesary....
parallel lines have the same slope so obsn 3 is sufficient..

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.

Hi,
I think its very straight..
if one observation can eliminate all wrong choices, other observations are not necessary..
arent you required to check for slope..
if any other set of line ,other than llel lines, also has property of same slopes, only then you may require to use other obsn to eliminate choices..

Attached is a visual that should help.

Here is an algebraic approach

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

To practise ten 700+ Level Number Properties Questions attempt the The E-GMAT Number Properties Knockout

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

Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1

Hello GMATinsight

Please help. I have some doubts about your observations.

Observation1 : How you have identified line is moving upward. I can't see any arrow in the line.

Observation3: How you have identified this? Is this a formula?

Thank you.

760Abhi

1) We always observe a line from Left to right. This line is moving upwards when observed from left to right.
2) Slope of Any line \(= \frac{Rise}{Run} = \frac{y_2 - y_1}{x_2 - x_1}\) yes it's a basic about slope and hence a formula

This line is passing through two points (0,2) and (-3,0)
hence Slope \(= \frac{0-2}{-3-0} = \frac{2}{3}\)

I hope this help!



1st Video solutions based Modular On-Demand QUANT Course: All Concepts | 2000+Qns | 20+ Tests |
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub

[="GMATinsight"]

760Abhi

1) We always observe a line from Left to right. This line is moving upwards when observed from left to right.
2) Slope of Any line \(= \frac{Rise}{Run} = \frac{y_2 - y_1}{x_2 - x_1}\) yes it's a basic about slope and hence a formula

This line is passing through two points (0,2) and (-3,0)
hence Slope \(= \frac{0-2}{-3-0} = \frac{2}{3}\)

I hope this help!



1st Video solutions based Modular On-Demand QUANT Course: All Concepts | 2000+Qns | 20+ Tests |
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub [/quote]


It really helps.

Thank you so much for your quick reply.

↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧




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



Let's find the slope of line l first. l passes through the points (0,2) and (-3,0) and we know that

Slope of the line passing through the points \((x_1, y_1)\) and \((x_2, y_2)\) is given by, m = \(\frac{y_2 - y_1}{x_2 - x_1}\)
=> m = \(\frac{2 - 0 }{ ( 0 - (-3))}\) = \(\frac{2}{3}\)

We also know that if two lines are parallel then their slopes will be equal
=> Slope of the parallel line will also be \(\frac{2}{3}\)

Now, we need to find which of the lines given in the option choices has slope of \(\frac{2}{3}\)
We know that Slope of a general line ax + by + c = 0 is given by -(Coefficient of x) / (Coefficient of y) = \(\frac{-a}{b}\) = \(\frac{2}{3}\)

=> a can be -2 and b can b can be 3 or a can be 2 and b can be -3 or other choices.
=> line will be -2x + 3y = 0 or 2x - 3y = 0 or 3y - 2x = 0

So, Answer will be A
Hope it helps!

Watch the following video to learn the Basics of Co-ordinate Geometry