Question 21272
First you have to find the slope of line AB.  
{{{m= (y[2]-y[1])/(x[2]-x[1]) }}}
{{{m=(10-6)/(-4-2)=4/-6=-2/3}}}


The equation of the line is in the form y=mx+b, where m is the slope that you just found, (x,y) represents any point on the line, either point A(2,6) or B(-4,10).


Use:  {{{m=-2/3}}}, x=2, and y=6, and solve for b.
y=mx+b
{{{6=(-2/3)*2 + b}}}


Multiply both sides by the denominator, which is 3
{{{3*6=3*(-2/3)*2 + 3*b}}}
{{{18 = -4 + 3b}}}
{{{22= 3b}}}
{{{b = 22/3}}}


Final Answer:  
{{{y = mx + b}}}
{{{y= (-2/3)x +22/3 }}}


Check:  Substitute the values of B(-4,10), and see if it works:

{{{y = (-2/3)x + 22/3}}}
{{{10 = 8/3 + 22/3 }}}
{{{10 =30/3 }}}  
It checks! 


What about point C(8,15)??  You asked for the equation of line AB, and it seems that point C is just another point.  Perhaps it was to be used in a different problem.  


NOTE:  Math is not usually as hard as it sometimes looks!  Don't let anyone blow you away by making it look harder than it really is.  It should NOT be intimidating!!


R^2 at SCC