Question

Write an equation of the line that is parallel to 5x + 20y = 10 and passes through the point (8, 3).

Answer 1

$5x+20y=10\implies y=\dfrac12-\dfrac x4$

is a line with slope $-\dfrac14$. Any line parallel to it will have the same slope. Using the point-slope formula, the equation of the parallel line passing through (8, 3) is

$y-3=-\dfrac14(x-8)\implies y+\dfrac13x=5\implies x+3y=15$