Why is the slope intercept form of the function that contains the points (5,6) and (9,14)?
y=+

First let us find the slope of the line using the two points (5,6), (9,14) given.
x1 = 5, y1 = 6,  x2 = 9, y2 =14

m = (y2 - y1)/(x2 - x1). 
m = (14 - 6)/(9 - 5).
m = 8/4 = 2.
Therefore  slope, m = 2.

Using y = mx + c.  Slope = m,  m = 2.
y = 2x + c

Substituting any of  the point (5,6) into  the equation,  x = 5, y = 6.
6 = 2(5) + c
6 = 10 + c
6-10 = c
-4 = c
c = -4.  Substituting into y = mx + c,  m =2,  c = -4
Therefore  y = 2x + (-4).
y = 2x - 4.
Cheers.