dvk007 wrote:

In the xy-coordinate system, if (a, b) and (a – 4, b + k) are two points on the line x = 2y + 8, then what is the value of k?

A. –4

B. –2

C. 1/2

D. 1

E. 4

Key Concept: If a point lies on a given line (or curve), then the x- and y-coordinates of that point must satisfy the equation of that line (or curve) So, we can conclude that:

x = a and y = b is a solution to the equation x = 2y + 8

and

x = a–4 and y = b+k is a solution to the equation x = 2y + 8

Let's deal with each case.

If x = a and y = b is a solution to the equation x = 2y + 8, then we can replace x and y with a and b

We get: a = 2b + 8

Rewrite as:

a - 2b = 8If x = a–4 and y = b+k is a solution to the equation x = 2y + 8, then we can replace x and y with a-4 and b+k

We get: a-4 = 2(b+k) + 8

Expand: a - 4 = 2b + 2k + 8

Add 4 to both sides to get: a = 2b + 2k + 12

Subtract 2b from both sides:

a - 2b = 2k + 12We now have two equations:

a - 2b = 2k + 12a - 2b = 8Subtract the bottom equation from the top equation to get: 0 = (2k + 12) - 8

Simplify: 0 = 2k + 4

So: -4 = 2k

Solve: k = -2

Answer: B

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

Sign up for my free GRE Question of the Day emails