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Math Expert V
Joined: 02 Sep 2009
Posts: 58991
In the xy-coordinate plane, the points (a, b ) and (a + k, b – 3) are  [#permalink]

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Difficulty:   15% (low)

Question Stats: 85% (01:28) correct 15% (02:09) wrong based on 89 sessions

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In the xy-coordinate plane, the points (a, b ) and (a + k, b – 3) are on the line defined by y = 2x – 5. What is the value of k ?

(A) -5/2
(B) -5/3
(C) -3/2
(D) -2/3
(E) -2/5

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Math Expert V
Joined: 02 Sep 2009
Posts: 58991
Re: In the xy-coordinate plane, the points (a, b ) and (a + k, b – 3) are  [#permalink]

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Bunuel wrote:
In the xy-coordinate plane, the points (a, b ) and (a + k, b – 3) are on the line defined by y = 2x – 5. What is the value of k ?

(A) -5/2
(B) -5/3
(C) -3/2
(D) -2/3
(E) -2/5

Similar questions:
https://gmatclub.com/forum/in-the-xy-co ... 35012.html
https://gmatclub.com/forum/in-the-xy-co ... 55642.html
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Re: In the xy-coordinate plane, the points (a, b ) and (a + k, b – 3) are  [#permalink]

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Bunuel wrote:
In the xy-coordinate plane, the points (a, b ) and (a + k, b – 3) are on the line defined by y = 2x – 5. What is the value of k ?

(A) -5/2
(B) -5/3
(C) -3/2
(D) -2/3
(E) -2/5

Since there is a specific rule which leads to a straightforward calculation, we'll just use it.
This is a Precise approach.

When we're given two points, we can calculate the slope of the line through them with (y2 - y1)/(x2 - x1).
So, 2 = (b - 3 - b)/(a + k - a) = -3/k.
Then k = -3/2.

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GMAT 1: 790 Q51 V49 GRE 1: Q170 V170 Re: In the xy-coordinate plane, the points (a, b ) and (a + k, b – 3) are  [#permalink]

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Bunuel wrote:
In the xy-coordinate plane, the points (a, b ) and (a + k, b – 3) are on the line defined by y = 2x – 5. What is the value of k ?

(A) -5/2
(B) -5/3
(C) -3/2
(D) -2/3
(E) -2/5

Points with variables, plus a line equation, makes me think that this is just an algebra problem dressed up in geometry clothing. After all, if a point is on a line, and you have the equation for that line, all that means is that you can plug in the coordinates of the point, to the equation for the line, and you get a true statement.

So, we can plug in both points and get correct equations:

b = 2a - 5
b-3 = 2(a+k) - 5

Simplify the second equation:

b - 3 = 2a + 2k - 5

b = 2a + 2k - 2

Since both equations now tell you the value of b, you can set them equal to each other:

2a - 5 = 2a + 2k - 2
-5 = 2k - 2
-3 = 2k
k = -3/2
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Re: In the xy-coordinate plane, the points (a, b ) and (a + k, b – 3) are  [#permalink]

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Bunuel wrote:
In the xy-coordinate plane, the points (a, b ) and (a + k, b – 3) are on the line defined by y = 2x – 5. What is the value of k ?

(A) -5/2
(B) -5/3
(C) -3/2
(D) -2/3
(E) -2/5

$$b = 2a - 5,$$
$$b - 3 = 2(a+k) - 5... K = -3/2$$
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Re: In the xy-coordinate plane, the points (a, b ) and (a + k, b – 3) are  [#permalink]

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Bunuel wrote:
In the xy-coordinate plane, the points (a, b ) and (a + k, b – 3) are on the line defined by y = 2x – 5. What is the value of k ?

(A) -5/2
(B) -5/3
(C) -3/2
(D) -2/3
(E) -2/5

We have two points and an equation of a straight line.

Points : (a,b) & (a+k), (b-3)

Equation of a straight line :$$y = 2x – 5$$, in which 2 is slope and -5 is y - intercept

Formula says, $$m = \frac{Y2 - Y1}{X2 - X1}$$

$$2 = \frac{b - 3 - b}{a + k - a}$$

$$2 = \frac{- 3}{k}$$

$$k = \frac{-3}{2}$$
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Re: In the xy-coordinate plane, the points (a, b ) and (a + k, b – 3) are  [#permalink]

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_________________ Re: In the xy-coordinate plane, the points (a, b ) and (a + k, b – 3) are   [#permalink] 08 Sep 2019, 07:38
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