To find the value of k in the equation x = 3y - 7 for the given points (a, b) and (a + 3, b + k), we can substitute the coordinates of the points into the equation and solve for k.
Let's substitute the coordinates of the points into the equation:
For the point (a, b):
a = 3b - 7 ---- (1)
For the point (a + 3, b + k):
a + 3 = 3(b + k) - 7 = 3b + 3k - 7
a - 3b = 3k - 10 ---- (2)
Now, we can solve equations (1) and (2) simultaneously to find the value of k.
From equation (1), we can rewrite it as:
a - 3b = -7
Substituting this into equation (2):
-7 = 3k - 10
3k = -7 + 10
3k = 3
k = 1
Therefore, k = 1. The answer is D