dave13 wrote:

wings.ap wrote:

Bunuel wrote:

[qimg]http://gmatclub.com/forum/download/file.php?id=28160[/img]

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.Attachment:

2015-10-22_0824.png

Okay here is a very simple solution but you must understand that slope = rise or drop in y axis/run of x axis.(always take absolute value of x)

Now here slope = rise/run=2/3. Parallel line will also have same slope.

Check A bcz it is the easiest to check for. ... well we have a slope of 2/3. We don't even have to look at any other option.

Answer is

ARemember in PS there is only one unique solution to the problem.Hello. I understand you find slope through y2-y1/x2-x1 but how manage to choose the correct answer from answer options ok yes we know slope is 2/3 so what ?

" y= 2/3x+0 " How do you know that Y-intercept is zero. and how from this y= 2/3x+0 I can convert into the equation matching one of answer choices ? can you please explain ?

dave13We know the y-intercept is 0 because we are

rewriting the answer's equations into slope-intercept form.

Slope-intercept form of a line's equation is

\(y = mx + b\)

\(m\) = slope

\(b\)= y-intercept

x-coefficient = m = slope

I am "converting" (your word) the answer choices

Then I can find

slope = m = coefficient of x. I can also find the y-intercept. I simply move terms around and isolate y. I make y's coefficient = 1. (In \(y = mx + b\), y has a coefficient of 1)

Rewriting all answer choices in slope-intercept form:

A) 3y − 2x = 0Add 2x to both sides: 3y = 2x + 0

Make y's coefficient 1 by dividing ALL terms by 3:

\(\frac{3y}{3}\) = \(\frac{2}{3}\) x + \(\frac{0}{3}\)

\(y = \frac{2}{3}x + 0\), OR

\(y = \frac{2}{3}x\)

(B) 3y + 2x = 03y = - 2x + 0

y = - 2/3 x + 0/3

\(y = -\frac{2}{3}x\)

(C) 3y + 2x = 63y = -2x + 6

y = -2/3 x + 6/3

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

(D) 2y − 3x = 62y = 3x + 6

y = 3/2x +6/2

\(y = \frac{3}{2} x + 3\)

(E) 2y + 3x = −62y = - 3x - 6

y = - \(\frac{3}{2}\) x - 6/2

\(y = - \frac{3}{2} x - 3\)

ANSWER A is the only one with slope = m = \(\frac{2}{3}\). It is parallel to diagram's line.

To try to answer your second question:

\(y =\frac{2}{3}x\) <=> \(y= \frac{2}{3}x\)

+ 0+0 = +b

No +b? Then "+0" is implied.

And see below.** No +b means the line runs through the origin. There IS a y-intercept. It's 0. It's not "written out."

** Lines that run through the origin have x- and y-intercepts of 0. If there seems to be no y-intercept in an equation, as in y = \(\frac{2}{3}\)x?

The y-intercept = 0. It could be written explicitly. In very literal slope-intercept form, y = mx + b:

\(y = \frac{2}{3}x\) could be written:

\(y =\frac{2}{3} x + 0\)

Set x equal to zero to find y-intercept: y = (0) + 0

y = 0 when x = 0

(0, 0) Y INTERCEPT

Set y equal to zero to find x-intercept: 0 =\(\frac{2}{3}\) x + 0

x = 0 when y = 0

(0,0) X INTERCEPT

That math is identical to the math needed for y = \(\frac{2}{3}\)x. Find intercepts by setting x and y equal to 0. y-intercept:

y = \(\frac{2}{3}\)*(0)

y = 0 when x = 0

x-intercept: (0) = \(\frac{2}{3}\) x

x-intercept = 0You might want to take a look at

Bunuel ,

Coordinate Geometry, Point-intercept form ("Point-intercept" a.k.a. slope intercept)

Maybe I don't understand what you are asking. If not, try again, my mistake.

Hope that helps.

_________________

SC Butler has resumed!Get

two SC questions to practice, whose links you can find by date,

here.Tell me, what is it you plan to do with your one wild and precious life? --

Mary Oliver