Point r has coordinates (1,3), and point s has coordinates (6,y). if the distance from r to s is 13 units, what are the possible values of y?

Using distance formula:

(6-1)² + (y-3)² = 13²
5² + y² - 6y + 9 = 169
25 + y² - 6y + 9 - 169 = 0
y² - 6y - 135 = 0
y² + 9y - 15y - 135 = 0
y(y + 9) - 15(y + 9) = 0
(y + 9)(y - 15) = 0
y+9 = 0     or     y-15 = 0 
y = -9                y = 15

y=-9 and y=15

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