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3x + y + 1 = 0y = - 3x - 12x - 3y + 8 = 03y - 2x - 8 = 03y = 2x + 8y = 2x/3 + 8/3-3x - 1 = 2x/3 + 8/3-9x - 3 = 2x + 8-11x = 11x = -1y = -3x - 1 = 3 - 1 = 2The graphs intersect at the point (-1, 2).
If: y = x^2 +2x +2 and y = 7 -2x Then: x^2 +2x +2 = 7 -2x Transposing terms: x^2 +4x -5 = 0 Factorizing the above: (x +5)(x -1) = 0 meaning x = -5 or x = 1 By substitution into original equations points of intersection are at: (-5, 17) and (1, 5)
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Perpendicular equation: x+2y = 0 Point of intersection: (2, -1) Perpendicular distance: square root of 5