Question

Write the equation of the line that passes through (2, 3) and is parallel to the line 12x – 5y = 2.

Answer 1

$k:12x-5y=2\to-5y=-12x+2\ \ \ /:(-5)\to y=\frac{12}{5}y-\frac{2}{5}\\\\l:y=mx+b\\\\k\ ||\ l\iff m=\frac{12}{5}\\\\ l:y=\frac{12}{5}x+b;\ (2;\ 3)\\\\\frac{12}{5}\cdot2+b=3\\\\\frac{24}{5}+b=3\\\\b=\frac{15}{5}-\frac{24}{5}\\\\b=-\frac{9}{5}\\\\Answer:y=\frac{12}{5}x-\frac{9}{5}\to\frac{12}{5}x-y=\frac{9}{5}\ \ \ \ /\cdot5\to12x-5y=9$