Modelling with Straight Lines (AQA A-Level Mathematics): Flashcards

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Modelling with Straight Lines
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Gradient mm formula using (x1,y1)(x_1,y_1) and (x2,y2)(x_2,y_2)

m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

Gradient as ΔyΔx\frac{\Delta y}{\Delta x} equals

y2−y1x2−x1\frac{y_2 - y_1}{x_2 - x_1}

Midpoint formula for endpoints (x1,y1)(x_1,y_1) and (x2,y2)(x_2,y_2)

(12(x1+x2),12(y1+y2))\left(\frac{1}{2}(x_1+x_2), \frac{1}{2}(y_1+y_2)\right)

Midpoint represents what of the coordinates?

Mean of the xx and yy coordinates

Length formula for endpoints (x1,y1)(x_1,y_1) and (x2,y2)(x_2,y_2)

(x2−x1)2+(y2−y1)2\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}

Name of formula (x2−x1)2+(y2−y1)2\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}

Distance formula

Equation of line with gradient −2-2 through (3,5)(3,5)

y=−2x+11y = -2x + 11

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