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
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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)|)))
