Question

Write the equation of the line that is parallel to the line 4x − 3y = −12 and passes through the point (−3, 4) .

Answer 1

4x - 3y = -12 => 3y = 4x + 12 => y = 4/3 x + 4 => slope is 4/3

Parallel lines have equal slope.
i.e. required equation is (y - 4)/(x - (-3)) = 4/3 => (y - 4)/(x + 3) = 4/3 => 3(y - 4) = 4(x + 3) => 3y - 12 = 4x + 12 => 4x - 3y = -24