#color(blue)("Using short cuts - part calculation")#
We need to have a single #y# with no coefficient. So divide everything by 12. So #14x->14/12x = 7/6x#
As #-12y# is on the right and we would need to move it to the left to get +y on its own the #+14x# is on the correct side.
So #14x->14/12x = 7/6x# is on the correct side and positive
So the slope is #+7/6#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Using first principles - full calculation")#
#color(purple)("The Short Cut method uses First Principles but")#
#color(purple)("skips steps so it is faster.")#
You need to change this into the format of
#y = mx + c" "# where m is the slope (gradient")
Multiply both sides by #(-1)# making the #y# term positive.
#-8=+12y-14x#
Add #14x# to both sides giving
#color(brown)(-8color(blue)(+14x)=12y-14xcolor(blue)(+14x)) #
#-8+14x=12y+0#
Divide both sides by #color(blue)(12)#
#color(brown)(-8/(color(blue)(12)) +(14x)/(color(blue)(12))=12/(color(blue)(12))xxy#
#color(green)(y=7/6 x-2/3)#
#color(green)(ul(bar(|color(white)(2/2)m=7/6color(white)(2/2)|)))#
