This strand combines coordinate geometry with function graphing. Students learn to work with straight lines, plot and interpret curves, and use graphical methods to solve equations.
Equation y = mx + c: m is gradient (slope), c is y-intercept. Gradient = rise/run = (y₂−y₁)/(x₂−x₁). Parallel lines have equal gradients. Perpendicular lines: m₁ × m₂ = −1. Finding equation given gradient and a point, or two points. Midpoint: ((x₁+x₂)/2, (y₁+y₂)/2). Distance: √((x₂−x₁)² + (y₂−y₁)²).
Plot by substituting x-values into function and plotting (x, y) points. Quadratic y = ax² + bx + c: parabola. Cubic y = ax³: S-shaped curve. Reciprocal y = a/x: two branches with asymptotes at axes. Exponential y = aˣ: rapid growth/decay curve. Identify key features: intercepts, turning points, asymptotes, symmetry.
Solving equations graphically: where the curve crosses y = 0 (roots) or where two curves intersect. Estimating gradient at a point by drawing a tangent line (Extended). Finding area under a curve using trapezoids (Extended). Using graphs to solve simultaneous equations.
Draw a tangent line to the curve at the given point (a straight line that just touches the curve). Then find the gradient of this tangent by choosing two points on it and calculating rise/run. This is an estimation — the accuracy depends on how well you draw the tangent. This skill is Extended only and prepares you for calculus at A Level.
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