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The equation of a straight line containing the points (10,100) and (15

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The equation of a straight line containing the points (10,100) and (15 [#permalink]

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New post 30 Oct 2017, 23:55
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Question Stats:

97% (01:02) correct 3% (01:58) wrong based on 34 sessions

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The equation of a straight line containing the points (10,100) and (15, 60) is

(A) y = –8x + 180
(B) y = 8x – 180
(C) y = x/8 + 7.5
(D) y = –8x – 180
(E) y = –x/8 + 22.5
[Reveal] Spoiler: OA

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The equation of a straight line containing the points (10,100) and (15 [#permalink]

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New post 31 Oct 2017, 08:21
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A wins.

Eq. is y = mx + b

m = (y2- y1)/(x2-x1) = (60-100)/(15-10) = -8

b is value of y when x = 0.
Here, x reduces from 15 to 10 when y increases from 60 to 100. So, x will become 0 when y increases by 80.
New y = 100 + 80 = 180

Hence, y = -8x + 180

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The equation of a straight line containing the points (10,100) and (15 [#permalink]

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New post 31 Oct 2017, 09:17
Bunuel wrote:
The equation of a straight line containing the points (10,100) and (15, 60) is

(A) y = –8x + 180
(B) y = 8x – 180
(C) y = x/8 + 7.5
(D) y = –8x – 180
(E) y = –x/8 + 22.5

We need point slope form of the line equation.

\(y = mx + b\), \(m\) = slope, \(b\) = y-intercept

1) Find slope of line from coordinates of the two given points:

\(\frac{rise}{run}=\frac{(100-60)}{10-15}=\frac{40}{-5}= -8 =\) slope

\(y = -8x + b\)

2. Find \(b\) using (x,y) from either given point

\(100 = -8(10) + b\)
\(b = 180\)
b is positive; the + sign on RHS stays the same

3) Final: \(y = -8x + 180\)

Answer A

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Re: The equation of a straight line containing the points (10,100) and (15 [#permalink]

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New post 31 Oct 2017, 10:00
Expert's post
Top Contributor
Bunuel wrote:
The equation of a straight line containing the points (10,100) and (15, 60) is

(A) y = –8x + 180
(B) y = 8x – 180
(C) y = x/8 + 7.5
(D) y = –8x – 180
(E) y = –x/8 + 22.5


Notice that all of the answers are expressed in slope y-intercept form (y = mx + b, where m represents the line's slope and b represents the line's y-intercept)
We can use this to our advantage.

First let's sketch the two points and connect them with a line...
Image

First notice that the slope of the line is NEGATIVE
So, we can ELIMINATE answer choices B and C, since those equations represent lines with POSITIVE slopes

Next notice that the y-intercept will be POSITIVE
So, we can ELIMINATE answer choice D, since that equation represents a line with a NEGATIVE y-intercept

We're left with answer choices A and E
The slope of answer choice A (y = –8x + 180) is -8, and the slope of answer choice E (y = –x/8 + 22.5) is -1/8

From our sketch, we can see that the line is quite steep, so we can ELIMINATE answer choice E, since a slope of -1/8 is not very steep.

Answer: A

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Re: The equation of a straight line containing the points (10,100) and (15   [#permalink] 31 Oct 2017, 10:00
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