In the x y-coordinate plane, the points (a, b) and (a + k, b – 3) are on the line defined by y = 2 x – 5. What is the value of k? (A) -5/2 (B) -5/3 (C) -3/2 (D) -2/3 (E) -2/5 [spoiler]Source: https://readyforgmat.com[/spoiler]

Point (a,b) is on the line y = 2x -5, then b = 2a -5 Point (a+k, b-3) is also on that line then: b-3 = 2(a+k) -5 or b -3 = 2a + 2k - 5 Then b = 2a + 2k -2 Subtract the second bold equation to the first one: 2a + 2k - 2 - (2a -5) = b- b = 0 2k + 3 = 0 then k =-3/2 Pick C.

Alternative solution using slope = (y2-y1 / x2-x1) and the fact the the slope of the line is 2 (the coefficient 'a' for x in the equation y=ax+b) (b-3) - b / (a+k) - a = -3 / k, and that equals 2, so -3/k = 2 k=-3/2. Pick C.

sanju09 wrote:In the x y-coordinate plane, the points (a, b) and (a + k, b – 3) are on the line defined by y = 2 x – 5. What is the value of k? (A) -5/2 (B) -5/3 (C) -3/2 (D) -2/3 (E) -2/5 [spoiler]Source: https://readyforgmat.com[/spoiler] slope of the line = [(b-3) - b] / [(a+k)-a] = -3/k form the eq.( y = 2 x - 5) slope = 2 so, -3/k=2 k= -3/2

sanju09 wrote:In the x y-coordinate plane, the points (a, b) and (a + k, b – 3) are on the line defined by y = 2 x – 5. What is the value of k? (A) -5/2 (B) -5/3 (C) -3/2 (D) -2/3 (E) -2/5 C- -3/2

limestone wrote:Point (a,b) is on the line y = 2x -5, then b = 2a -5 Point (a+k, b-3) is also on that line then: b-3 = 2(a+k) -5 or b -3 = 2a + 2k - 5 Then b = 2a + 2k -8 From the 2 bold equations, 2k - 8 must be equal to -5 or 2k = -5 +8 = -3 k =-3/2 Pick C. How do we get k = -3/2 from 2 a - 5 = 2 a + 2 k - 8?

Well, I made a mistake here. Sorry guys. b is not equal to 2a + 2k - 8 as I stated above b-3 = 2(a+k) -5 or b = 2a + 2k -5 +3 or b = 2a + 2k -2 Also : b = 2a -5 then 2a -5 = 2a + 2k -2 or 2k = -3 or k=-3/2 I have also edited my answer above.

This is what I did (a,b)=(x,y) x=a+k y=b-3 original equation is y=2x-5,so... b-3=2(a+k)-5 Then I started solving the equation for k b-3+5=2(a+k) b+2=2(a+k) (b+2)/2 = a + k ((b+2)/2)-a = k combine everything into one fraction (b+2-2a)/2=k I picked a coordinate (0,-5) that would satisfy y=2x-5 and plugged it in (-5+2-2*0)/2 = k (-5+2-0)/2 = k -3/2 = k *looks like a long process but when you are writing it down it is much faster than it seems*