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Simplifying (1 + -1k) * x + -1y + 3 = 0 Reorder the terms for easier multiplication: x(1 + -1k) + -1y + 3 = 0 (1 * x + -1k * x) + -1y + 3 = 0 Reorder the terms: (-1kx + 1x) + -1y + 3 = 0 (-1kx + 1x) + -1y + 3 = 0 Reorder the terms: 3 + -1kx + 1x + -1y = 0 Solving 3 + -1kx + 1x + -1y = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -1kx + 1x + -3 + -1y = 0 + -3 Reorder the terms: 3 + -3 + -1kx + 1x + -1y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1kx + 1x + -1y = 0 + -3 -1kx + 1x + -1y = 0 + -3 Combine like terms: 0 + -3 = -3 -1kx + 1x + -1y = -3 Add '-1x' to each side of the equation. -1kx + 1x + -1x + -1y = -3 + -1x Combine like terms: 1x + -1x = 0 -1kx + 0 + -1y = -3 + -1x -1kx + -1y = -3 + -1x Add 'y' to each side of the equation. -1kx + -1y + y = -3 + -1x + y Combine like terms: -1y + y = 0 -1kx + 0 = -3 + -1x + y -1kx = -3 + -1x + y Divide each side by '-1x'. k = 3x-1 + 1 + -1x-1y Simplifying k = 3x-1 + 1 + -1x-1y Reorder the terms: k = 1 + 3x-1 + -1x-1y
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