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.