"(1) \\hspace{0.1cm}y = mx + c \\hspace{0.1cm} \\textsf{is the equation of a}\\\\\\textsf{straight line in the gradient(slope) - intercept form}\\\\\n\n\\textsf{y-intercept of}\\hspace{0.1cm}6\\hspace{0.1cm}\\textsf{means at}\\hspace{0.1cm} x = 0, y = 6. \\\\\n\n\ny = mx + c, m = 6 \\hspace{0.1cm}(is \\hspace{0.1cm}given)\\\\\n\n\n\n\\textsf{at}\\hspace{0.1cm} x = 0, y = 6 \\\\\n\n\n\\Rightarrow y = 6 = m(0) + c, c = 6.\\\\\n\n\n\\therefore y = 10x + 6\\hspace{0.1cm} \\textsf{is the required equation}\\\\\n\n\n(2) \\hspace{0.1cm}\\textsf{Similarly,}\\hspace{0.1cm} c = -11\\\\\n\n\n\\textsf{But, since the line is perpendicular}\\\\\\textsf{to a line whose gradient is 5, therefore,}\\\\\\textsf{we must apply the condition of perpendicularity.}\\\\\\textsf{That is, the product of the two}\\\\\\textsf{gradients is equal to}\\hspace{0.1cm} -1.\\\\\n\n\\therefore m = -\\frac{1}{5}\\\\\\Rightarrow y = -\\frac{1}{5}x - 11"
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