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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: 47898
A line segment containing the point (0,0) and (12,8) will also contain  [#permalink]

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11 Dec 2017, 23:07
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Difficulty:

15% (low)

Question Stats:

76% (00:34) correct 24% (00:51) wrong based on 82 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)

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

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12 Dec 2017, 12:59
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.

*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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08 May 2018, 11:38
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.

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Re: A line segment containing the point (0,0) and (12,8) will also contain &nbs [#permalink] 08 May 2018, 11:38
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