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

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SVP
Joined: 12 Sep 2015
Posts: 2140
Re: The graph of which of the following equations is a straight line that [#permalink]

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28 Aug 2017, 13:28
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Bunuel wrote:

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.

[Reveal] Spoiler:
Attachment:
2015-10-22_0824.png

If two lines are parallel, then they have the SAME SLOPE.

The given line passes through the points (0, 2) and (-3, 0)
Applying the slope formula, we get: Slope = (2 - 0)/(0 - -3)
= 2/3

Now take each equation of each line (in the answer choices) and rewrite it in slope y-intercept form: y = mx + b (where m = slope and b = y-intercept)

The rewritten equation that has m = 2/3, will be the correct answer....

A. 3y - 2x = 0...rewrite as y =(2/3)x + 0
DONE!
This line has a slope of 2/3, so it must be parallel with the given line.

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Re: The graph of which of the following equations is a straight line that [#permalink]

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25 Sep 2017, 21:41
If 2 lines are parallel then slope should be same,

Here slope of the given line=(y2-y1)/(x2-x1)
= (2-0)/(0-(-3) = 2/3

A. The equation should be in the form of y= mx+c where m is the slope
convert the equation in above form we will get y= 2/3x+0
so slope is 2/3 matching with the question stem equation so
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Joined: 09 Mar 2016
Posts: 323
The graph of which of the following equations is a straight line that [#permalink]

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24 Dec 2017, 07:51
wings.ap wrote:
Bunuel wrote:

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.

[Reveal] Spoiler:
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.
Remember 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 ?
Senior Manager
Joined: 09 Mar 2016
Posts: 323
Re: The graph of which of the following equations is a straight line that [#permalink]

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24 Dec 2017, 08:44
nkmungila wrote:
If 2 lines are parallel then slope should be same,

Here slope of the given line=(y2-y1)/(x2-x1)
= (2-0)/(0-(-3) = 2/3

A. The equation should be in the form of y= mx+c where m is the slope
convert the equation in above form we will get y= 2/3x+0
so slope is 2/3 matching with the question stem equation so

" 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 ? Thanks!
VP
Joined: 22 May 2016
Posts: 1416
The graph of which of the following equations is a straight line that [#permalink]

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24 Dec 2017, 19:11
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This post was
BOOKMARKED
dave13 wrote:
wings.ap wrote:
Bunuel wrote:
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.

[Reveal] Spoiler:
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.
Remember 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 ?

dave13

We 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

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 = 0

Add 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 = 0

3y = - 2x + 0
y = - 2/3 x + 0/3
$$y = -\frac{2}{3}x$$

(C) 3y + 2x = 6

3y = -2x + 6
y = -2/3 x + 6/3
$$y = - \frac{2}{3} x + 2$$

(D) 2y − 3x = 6

2y = 3x + 6
y = 3/2x +6/2
$$y = \frac{3}{2} x + 3$$

(E) 2y + 3x = −6

2y = - 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.

$$y =\frac{2}{3}x$$ <=> $$y= \frac{2}{3}x$$ + 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 = 0

You 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.
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The graph of which of the following equations is a straight line that   [#permalink] 24 Dec 2017, 19:11

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