Explanation

3x + 2y + 4 = 0 Rearrange: 2y = −3x − 4 Divide both sides by 2 y = (−3× − 4)/2 y = −3/2×−2 ∴ the gradient of the line 3x + 2y + 4 = 0 is −3/2 If two lines are perpendicular to each other ∴ m₁xm₂ = -1 Let m₁ =−3/2 ∴ m₂ = −1/m₁ = −1/(−3/2) = 2/3 From the equation of a line which is given as m = (y − y₁)/x − x₁) where (x₁, y₁) = (2, 3) ∴ 2/3 = (y − 3)/x − 2) =3(y - 3) = 2(x - 2) = 3y - 9 = 2 x -4 = 3y = 2 x -4 + 9 ∴ 3y = 2x + 5

3x + 2y + 4 = 0 Rearrange: 2y = −3x − 4 Divide both sides by 2 y = (−3× − 4)/2 y = −3/2×−2 ∴ the gradient of the line 3x + 2y + 4 = 0 is −3/2 If two lines are perpendicular to each other ∴ m₁xm₂ = -1 Let m₁ =−3/2 ∴ m₂ = −1/m₁ = −1/(−3/2) = 2/3 From the equation of a line which is given as m = (y − y₁)/x − x₁) where (x₁, y₁) = (2, 3) ∴ 2/3 = (y − 3)/x − 2) =3(y - 3) = 2(x - 2) = 3y - 9 = 2 x -4 = 3y = 2 x -4 + 9 ∴ 3y = 2x + 5