Equation of a Straight Line (AQA A-Level Mathematics): Flashcards

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Basic Coordinate Geometry
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Another name for the coordinate plane

Cartesian plane

Point where axes intersect, denoted as (0,0)(0, 0)

Origin

Distance formula between (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}

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

(x1+x22,y1+y22)\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)

Slope formula for points (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}

Slope-intercept form of a line equation

y=mx+cy = mx + c

What cc represents in y=mx+cy = mx + c

yy-intercept

Point-slope form for point (x1,y1)(x_1, y_1) with slope mm

y−y1=m(x−x1)y - y_1 = m(x - x_1)

Condition for two lines to be parallel

Same slope: m1=m2m_1 = m_2

Condition for two lines to be perpendicular

m1×m2=−1m_1 \times m_2 = -1

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