color(blue)("Using short cuts - part calculation")Using short cuts - part calculation
We need to have a single yy with no coefficient. So divide everything by 12. So 14x->14/12x = 7/6x14x→1412x=76x
As -12y−12y is on the right and we would need to move it to the left to get +y on its own the +14x+14x is on the correct side.
So 14x->14/12x = 7/6x14x→1412x=76x is on the correct side and positive
So the slope is +7/6+76
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color(blue)("Using first principles - full calculation")Using first principles - full calculation
color(purple)("The Short Cut method uses First Principles but")The Short Cut method uses First Principles but
color(purple)("skips steps so it is faster.")skips steps so it is faster.
You need to change this into the format of
y = mx + c" "y=mx+c where m is the slope (gradient")
Multiply both sides by (-1)(−1) making the yy term positive.
-8=+12y-14x−8=+12y−14x
Add 14x14x to both sides giving
color(brown)(-8color(blue)(+14x)=12y-14xcolor(blue)(+14x)) −8+14x=12y−14x+14x
-8+14x=12y+0−8+14x=12y+0
Divide both sides by color(blue)(12)12
color(brown)(-8/(color(blue)(12)) +(14x)/(color(blue)(12))=12/(color(blue)(12))xxy−812+14x12=1212×y
color(green)(y=7/6 x-2/3)y=76x−23
color(green)(ul(bar(|color(white)(2/2)m=7/6color(white)(2/2)|)))
