Question

write the standard form of the line that is parallel to 2x 3y = 4 and passes through the point (1, -4).

Answer 1

Parallel lines has equal slopes.
For line, 2x + 3y = 4
3y = -2x + 4
y = -2/3 x + 4/3
i.e. slope is -2/3

Equation of a line is given by y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

y - (-4) = -2/3 (x - 1)
y + 4 = -2/3 x + 2/3
3y + 12 = -2x + 2
2x + 3y = 2 - 12

Required equation in standard form is 2x + 3y = -10