The vertices of Triangle PQR are P(1, 2), Q(-3, 6) and

R(4, 8). A line through Q is parallel to line segment PR and passes through point (k, 14). Find k.

MY WORK:

I know that parallel lines have equal slopes. I first found the slope of line segment PR to be 2/1.

I then equated the slope this way:

2/1 = (14 - 2)/(k - 1)

Solving for k, I got k = 7 but the answer is k = 1.

What did I do wrong and why is the answer 1 not 7?