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# In the XY-plane, a line l passes through the origin and has a slope 3.

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Math Expert
Joined: 02 Sep 2009
Posts: 58335
In the XY-plane, a line l passes through the origin and has a slope 3.  [#permalink]

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16 Oct 2018, 04:52
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Difficulty:

25% (medium)

Question Stats:

70% (01:28) correct 30% (01:59) wrong based on 56 sessions

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In the XY-plane, a line l passes through the origin and has a slope 3. If points (1, a) and (b, 2) are on the line l, what is the value of a/b?

(A) 2
(B) 3
(C) 2/3
(D) 2/9
(E) 9/2

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Re: In the XY-plane, a line l passes through the origin and has a slope 3.  [#permalink]

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16 Oct 2018, 05:10
3
Bunuel wrote:
In the XY-plane, a line l passes through the origin and has a slope 3. If points (1, a) and (b, 2) are on the line l, what is the value of a/b?

(A) 2
(B) 3
(C) 2/3
(D) 2/9
(E) 92

A line l passes through the origin and has a slope 3

Slope of Origin (0,0) and (1, a) = (a-0)/(1-0)=3

a=3

Slope of Origin (0,0) and (b,2) = (2-0)/(b-0) =3

b=2/3

a/b= 3/(2/3) = 9/2

Bunuel Seems like typo Option E must be 9/2
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Joined: 02 Sep 2009
Posts: 58335
Re: In the XY-plane, a line l passes through the origin and has a slope 3.  [#permalink]

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16 Oct 2018, 05:12
NandishSS wrote:
Bunuel wrote:
In the XY-plane, a line l passes through the origin and has a slope 3. If points (1, a) and (b, 2) are on the line l, what is the value of a/b?

(A) 2
(B) 3
(C) 2/3
(D) 2/9
(E) 92

A line l passes through the origin and has a slope 3

Slope of Origin (0,0) and (1, a) = (a-0)/(1-0)=3

a=3

Slope of Origin (0,0) and (b,2) = (2-0)/(b-0) =3

b=2/3

a/b= 3/(2/3) = 9/2

Bunuel Seems like typo Option E must be 9/2

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Fixed. Thank you.
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Re: In the XY-plane, a line l passes through the origin and has a slope 3.  [#permalink]

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16 Oct 2018, 05:18
Bunuel wrote:
In the XY-plane, a line l passes through the origin and has a slope 3. If points (1, a) and (b, 2) are on the line l, what is the value of a/b?

(A) 2
(B) 3
(C) 2/3
(D) 2/9
(E) 9/2

line l passes through the origin and has a slope 3. If points (1, a) and (b, 2) are on the line l,

i,e. Slope of line using points (0,0) and (1,a) = (a-0)/(1-0) = 3

i.e. a = 3

Now, Slope of line using points (0,0) and (b,2) = (2-0)/(b-0) = 3

i.e. b = 2/3

i.e. a/b = 3/(2/3) = 9/2

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Re: In the XY-plane, a line l passes through the origin and has a slope 3.  [#permalink]

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16 Oct 2018, 11:51
Bunuel wrote:
In the XY-plane, a line l passes through the origin and has a slope 3. If points (1, a) and (b, 2) are on the line l, what is the value of a/b?

(A) 2
(B) 3
(C) 2/3
(D) 2/9
(E) 9/2

let (0,0) = $$(x_1,y_1)$$

$$slope = \frac{y_2 - y_1}{x_2 - x_1}$$

$$3 = \frac{a - 0}{1 - 0}$$

a = 3

then $$3 = \frac{2 - 0}{b - 0}$$

3b = 2

$$b = \frac{2}{3}$$

$$\frac{a}{b}$$ = $$3/\frac{2}{3}$$

$$\frac{a}{b}$$ = $$3 * \frac{3}{2}$$ = $$\frac{9}{2}$$

Re: In the XY-plane, a line l passes through the origin and has a slope 3.   [#permalink] 16 Oct 2018, 11:51
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