The points (x, y) represented in this table lie on a straight line. The point (13, q) lies on the same line. What is the value of p + q? Express your answer as a decimal to the nearest tenth. \(\begin{array}{c|c} x & y \\ \hline 2 & -5 \\ p & -14 \\ p+2 & -17 \\ \end{array}\)
+128475 We can equate slopes to find p
[ - 14 -- 5] [ -17 - - 5]
________ =__________ simplify
p - 2 (p + 2) - 2
[ -9] [ - 12 ]
____ = _______ cross- multiply
p - 2 p
-9p = -12 [ p - 2]
-9p = -12p + 24 add 12p to both sides
3p = 24 divide both sides by 3
p = 8
So...the slope = -12 / 8 = -3 / 2
So since the points ( 2, - 5) and ( 13, q) are on the same line....we have....
[q - - 5 ] -3
_______ = ___
13 - 2 2
[ q + 5 ] -3
______ = ___ cross-multiply
11 2
2 [ q + 5 ] = -3 * 11
2q + 10 = -33
2q = -43
q = -43 / 2
So p + q = 8 - 43/2 = [ 16 - 43 ] / 2 = -27/2 = -13.5
