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A line segment containing the point (0,0) and (12,8) will also contain

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A line segment containing the point (0,0) and (12,8) will also contain  [#permalink]

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New post 11 Dec 2017, 22:07
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

75% (00:55) correct 25% (01:18) wrong based on 87 sessions

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A line segment containing the point (0,0) and (12,8) will also contain  [#permalink]

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New post 12 Dec 2017, 11:59
1
Bunuel wrote:
A line segment containing the point (0,0) and (12,8) will also contain the point

(A) (2,3)
(B) (2,4)
(C) (3,2)
(D) (3,4)
(E) (4,2)

Given that one point is (0,0): If a line runs though the origin, its x- and y-intercepts = 0, and vice versa.

In slope-intercept form, the line's equation is
y = mx + b

in which m = slope and "+ b" is not written because
b = y-intercept = 0

Use the two points to find slope, \(\frac{rise}{run}\)

\(\frac{(y_1 - y_2)}{(x_1 -
x_2)}=\frac{(8-0)}{(12-0)}=\frac{8}{12}=\frac{2}{3}\) = slope

Line's equation is \(y=\frac{2}{3}x\)

That's straightforward. The y-coordinate must be 2/3 of the x-coordinate.

That is (3,2) Answer C

*Or, rewrite equation of line:
\(y=\frac{2}{3}x\)
\(3y=2x\)
\(3y - 2x = 0\)

Plug x and y from each answer into the equation. The pair that = 0 is the answer.
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Re: A line segment containing the point (0,0) and (12,8) will also contain  [#permalink]

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New post 08 May 2018, 10:38
Bunuel wrote:
A line segment containing the point (0,0) and (12,8) will also contain the point

(A) (2,3)
(B) (2,4)
(C) (3,2)
(D) (3,4)
(E) (4,2)


The slope of the line segment is (8 - 0)/(12 - 0) = 8/12 = 2/3. The equation of the line segment is:

y = (2/3)x + b

Substituting (0,0) we can determine b and we have:

b = 0

So the equation of the line segment is:

y = (2/3)x

We see that if x = 3, then y = 2. Thus (3, 2) is a point on the line segment.

Answer: C
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Re: A line segment containing the point (0,0) and (12,8) will also contain &nbs [#permalink] 08 May 2018, 10:38
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