D is the correct ans.

Both the coordinate points must lie on this line.
so by putting their values separately can lead us the answer.

i.e. put (a,b) on the equation you would get : a=3b-7
so by putting the other point (a+3, b+k) we get :

a+3=3(b+k)-7
=> a=3b+3k-10
now comparing with 1st equation : 3k-10=-7
and k=1

Hope this clears the doubt.

You can also rewrite the equation into the form of y = mx + b. Therefore:

y = x/3 + 7/3 the slope is 1/3

Now calculate the slope from given points.

(a,b) where a is x1 and b is y1

(a + 3, b + k) where a + 3 is x2 and b + k is y2

slope = y2 - y1/x2 - x1

slope = b + k - b/a + 3 - a
slope = k/3

Since both of the points lie on this line and the slope of this line is 1/3, then k/3 tells you that k = 1.

THank you guys for the help! ALeksander, i notice that you always think the way I think in re to math. I saw my mistake, I set the slope equal to 7/3 (y interecept) I should have nailed that question. Thanks for everything!