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

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Math Expert
Joined: 02 Sep 2009
Posts: 44599
A line segment containing the point (0,0) and (12,8) will also contain [#permalink]

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11 Dec 2017, 23:07
00:00

Difficulty:

25% (medium)

Question Stats:

71% (00:36) correct 29% (00:54) wrong based on 31 sessions

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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)
[Reveal] Spoiler: OA

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Joined: 22 May 2016
Posts: 1547
A line segment containing the point (0,0) and (12,8) will also contain [#permalink]

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12 Dec 2017, 12:59
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 one point is (0,0): When a line runs though the origin, its x- and y-intercepts = 0

In slope-intercept form, the line's equation is (y = mx + b), where 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
[Reveal] Spoiler:

*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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A line segment containing the point (0,0) and (12,8) will also contain   [#permalink] 12 Dec 2017, 12:59
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