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

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Math Expert
Joined: 02 Sep 2009
Posts: 44659
The equation of a straight line containing the points (10,100) and (15 [#permalink]

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30 Oct 2017, 23:55
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Difficulty:

25% (medium)

Question Stats:

88% (01:00) correct 12% (01:06) wrong based on 65 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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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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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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The equation of a straight line containing the points (10,100) and (15 [#permalink]

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31 Oct 2017, 10:00
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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...

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

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