M12 Coordinates and straight-line graphs mind map

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M12 Coordinates and straight-line graphs mind map

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Coordinates

Order: (x,y): horizontal then vertical; signs identify quadrant
Midpoint: Average corresponding coordinates; (−2,3),(6,7) → (2,5)

Gradient

Rise / run: Change in y ÷ change in x; subtract in same order
Special lines: y = k horizontal: m=0; x = k vertical: undefined m

Line equation

Form: y = mx+c; m gradient, c y-intercept; table checks plot
Find c: Use gradient and a point; through (2,5), m=3 → y=3x−1
Rearrange / parallel: Get y alone to read m; parallel lines share gradient

Perpendicular

Reciprocal: Higher: Non-zero finite gradients: m₁m₂ = −1
Example: Higher: Perpendicular to m=2 through (4,3): y = −x/2+5
Exception: Higher: Horizontal and vertical lines are perpendicular

Connections

Coordinates → Gradient: Coordinate changes give the gradient
Gradient → Line equation: Gradient and a point determine a line