Hi – I’m having a hard time with the following question. Can someone please help me out?

Geometry: p. 99 #69

In an xy-coordinate plane, a line is defined by y=kx+1. If (4,b), (a,4), and (a,b+1) are three points on the line, where a and b are unknown, then k=?

(A) ½
(B) 1
(C) 1 ½
(D) 2
(E) 2 ½

Using the three points given to us, we can put them in terms of the line's equation:

(4,b): b=4k+1
(a,4): 4=ak+1
(a,b+1): b+1=ak+1

From the last two, we can see that if ak+1=4 and ak+1=b+1, we can see that b+1=4, giving us a value of 3 for b. If we plug that into our first equation (b=4k+1), we can solve for k:

b=4k+1
3=4k+1
2=4k
2/4=k

1/2=k

Bill