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# The equation of the line graphed on the rectangular

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The equation of the line graphed on the rectangular [#permalink]  22 Aug 2018, 09:05
Expert's post
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Question Stats:

71% (00:56) correct 28% (00:50) wrong based on 103 sessions
Attachment:

xy.jpg [ 15.1 KiB | Viewed 2807 times ]

The equation of the line graphed on the rectangular XY plane above is:

$$y=\frac{8x}{9} + 3$$

 Quantity A Quantity B PO RO

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

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[Reveal] Spoiler: OA

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Re: The equation of the line graphed on the rectangular [#permalink]  29 Aug 2018, 03:48
2
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Carcass wrote:
Attachment:
xy.jpg

The equation of the line graphed on the rectangular XY plane above is:

$$y=\frac{8x}{9} + 3$$

 Quantity A Quantity B PO RO

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos for R.A.E

$$y=\frac{8x}{9} + 3$$

This can be written in : y = mx + c

$$y = \frac{8}{9} x + 3$$

So Slope m =$$\frac{Rise}{Run} = \frac{8}{9}$$

Now QTY A = PO = rise = 8

QTY B = RO = Run = 9

Therefore QTY A < QTY B
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Re: The equation of the line graphed on the rectangular [#permalink]  04 Jun 2020, 21:01
If Y=8/9x + 3 then surely the y-intercercept is =3

I, therefore, worked out PO=3?
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Re: The equation of the line graphed on the rectangular [#permalink]  06 Jun 2020, 13:01
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Re: The equation of the line graphed on the rectangular [#permalink]  06 Jun 2020, 14:42
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Expert's post
Carcass wrote:
Attachment:
xy.jpg

The equation of the line graphed on the rectangular XY plane above is:

$$y=\frac{8x}{9} + 3$$

 Quantity A Quantity B PO RO

Key concept #1: The point where a line intersects the x-axis will have a y-coordinate of 0
Key concept #2: The point where a line intersects the y-axis will have an x-coordinate of 0

Point R is the x-intercept.
So, according to Key concept #1, the y-coordinate of point R is 0
To find the corresponding x-coordinate, we'll plug y = 0 into the given equation to get: 0 = 8x/9 + 3
Subtract 3 from both sides of the equation to get: -3 = 8x/9
Multiply both sides of the equation by 9 to get: -27 = 8x
Divide both sides by 8 to get: x = -27/8
So the coordinates of point R are (-27/8, 0), which means RO = 27/8

Point P is the y-intercept.
So, according to Key concept #2, the x-coordinate of point R is 0
To find the corresponding y-coordinate, we'll plug x = 0 into the given equation to get: y = 8(0)/9 + 3
Evaluate to get: y = 3
So the coordinates of point P are (0, 3), which means PO = 3

We get:
QUANTITY A: 3
QUANTITY B: 27/8

Cheers,
Brent
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Re: The equation of the line graphed on the rectangular [#permalink]  06 Jun 2020, 14:47
1
KUDOS
Expert's post
Carcass wrote:
Attachment:
xy.jpg

The equation of the line graphed on the rectangular XY plane above is:

$$y=\frac{8x}{9} + 3$$

 Quantity A Quantity B PO RO

APPROACH #2:
If slope of the line were 1 (i.e., the equation of the line is y = x + 3), then PO and RO would be equal
Since the slope is actually LESS THAN 1, PO is shorter than RO.

Cheers,
Brent
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Re: The equation of the line graphed on the rectangular [#permalink]  07 Jun 2020, 10:28
1
KUDOS
GreenlightTestPrep wrote:
Carcass wrote:
Attachment:
xy.jpg

The equation of the line graphed on the rectangular XY plane above is:

$$y=\frac{8x}{9} + 3$$

 Quantity A Quantity B PO RO

Key concept #1: The point where a line intersects the x-axis will have a y-coordinate of 0
Key concept #2: The point where a line intersects the y-axis will have an x-coordinate of 0

Point R is the x-intercept.
So, according to Key concept #1, the y-coordinate of point R is 0
To find the corresponding x-coordinate, we'll plug y = 0 into the given equation to get: 0 = 8x/9 + 3
Subtract 3 from both sides of the equation to get: 3 = 8x/9
Multiply both sides of the equation by 9 to get: 27 = 8x
Divide both sides by 8 to get: x = 27/8
So the coordinates of point R are (27/8, 0), which means RO = 27/8

Cheers,
Brent

Hi Brent,
If we dont subtract 3 from both sides and solve simply we will get -27/8. Why it is not correct?
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Re: The equation of the line graphed on the rectangular [#permalink]  07 Jun 2020, 12:08
Expert's post
Farina wrote:
Hi Brent,
If we dont subtract 3 from both sides and solve simply we will get -27/8. Why it is not correct?

Good catch, Farina.
I have edited my response accordingly.

Cheers and thanks,
Brent
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Re: The equation of the line graphed on the rectangular [#permalink]  03 Jul 2020, 09:02
Thanks guys for the explanations.
Re: The equation of the line graphed on the rectangular   [#permalink] 03 Jul 2020, 09:02
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