Transcript Difficulty: Medium . In the figure, the slope of the line through points P and Q is the value of k? (a) 4 (b) 5 (c)

Difficulty: Medium
.
In the figure, the slope of the line through points P and Q is
the value of k?
(a) 4
(b) 5
(c) 6
(d) 7
(e) 8
. What is
B: K = 5
Explanation
The slope of a line in a coordinate plane is given by the fraction whose numerator is
the change in y between any two points on the line and whose denominator is the
change in x between the same points on the line.
The question asks for the value of k, which is the x-coordinate of point Q.
The change in y between points P and Q is 7 – 1 = 6. The change in x between these points
is k – 1. Since the slope is , it follows that
=
. Solving this equation gives 3k – 3
= 12. Therefore, 3k = 15, and k = 5.