Question 112937
The line equation passing through two points in the slope intercept form is given by:  


{{{( y - y1) = m (x - x1)}}} which is nothing but y = ax + b


Where m = {{{(y2 - y1)/(x2 - x1)}}}   (3, 4) and (5, 1) 


m = {{{(1 - 4)/(5 - 3)}}} 


==> m = {{{-3/2}}} 


Substituting in the line equation we get:  


(y - 4) = {{{-3/2}}} (x - 3)


==> 2y - 8 = -3x + 9 


==> 2y = -3x + 9 + 8


==> 2y = - 3x + 17 


==>  y = {{{ (-3/2)x + (17/2) }}}


thus the line equation


Hence, the solution