Find the equation of the line parallel to the line 3x – 4y ± 2 = 0

1.	Find the equation of the line parallel to the line 3x – 4y ± 2 = 0 and passing through the point (- 2, 3).
Answer» Given line is 3x - 4y + 2 = 0 ∴ Slope = - a/b = - (3/-4) = 3/4 = m ∴ Slope of the required line 3/4 (∴ required line is parallel to given line) Thus equation of the required line passing through (-2, 3) with slope 3/4 is, of the form y - y₁ = m(x - x₁) i.e, y - 3 = 3/4(x + 2) i.e., 4y - 12 = 3x + 6 i.e., 3x - 4y + 18 = 0

Find the equation of the line parallel to the line 3x – 4y ± 2 = 0 and passing through the point (- 2, 3).

Answer»

Given line is 3x - 4y + 2 = 0

∴ Slope = - a/b = - (3/-4) = 3/4 = m

∴ Slope of the required line 3/4

(∴ required line is parallel to given line)

Thus equation of the required line passing through (-2, 3) with slope 3/4 is, of the form

y - y₁ = m(x - x₁)

i.e, y - 3 = 3/4(x + 2)

i.e., 4y - 12 = 3x + 6

i.e., 3x - 4y + 18 = 0