Let the given point be #P_1->(color(green)(x_1),color(red)(y_1))=(color(green)(9),color(red)(-5))#
Let the gradient be #m=-1/3#
Using the standardised form #color(red)(y_1)=mcolor(green)(x_1)+c#
Where #c# is a constant
Then by substitution: #color(red)(-5)=(-1/3)(color(green)(9))+c#
but #-1/3xx9 = -3# giving:
#-5=3+c#
Add #color(magenta)(3)# to both sides
#color(green)(-5=-3+c color(white)("dd")->color(white)("dd")-5color(magenta)(+3)=-3color(magenta)(+3)+c)#
#color(green)(color(white)("ddddddddddddd")-> color(white)("dddd")-2color(white)("d")=color(white)("dddd")0color(white)("d")+c#
Thus #c=-2# so the finished equation is:
#y=-1/3x-2#
