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

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Solution

Equation of any line which is parallel to the line 3x - 4y + 2 = 0 is 3x - 4y + k = 0

Since this line passes through point (-2, 3),

$∴ 3 \times - 2 - 4 \times 3 + k = 0 \Rightarrow - 6 - 12 + k = 0$

$\Rightarrow k = 18$

Thus equation of required line is

3x - 4y + 18 = 0.

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

Equation of any line which is parallel to the line 3x - 4y + 2 = 0 is 3x - 4y + k = 0 Since this line passes through point (-2, 3), ∴ 3×−2−4×3+k=0⇒−6−12+k=0 ⇒ k=18 Thus equation of required line is 3x - 4y + 18 = 0.

Equation of any line which is parallel to the line 3x - 4y + 2 = 0 is 3x - 4y + k = 0

Since this line passes through point (-2, 3),

$∴ 3 \times - 2 - 4 \times 3 + k = 0 \Rightarrow - 6 - 12 + k = 0$

$\Rightarrow k = 18$

Thus equation of required line is

3x - 4y + 18 = 0.