Which of the following equations can be a normal to the line 4x – 3y + 6 = 0 ?

CONCEPT:

Slope – Intercept Form:

The slope – intercept form of a line is given as: y = m ⋅ x + c, where m is the slope of the line and c is called the intercept made by the line on the Y – axis.

Note: If two lines are perpendicular then product of their slopes is – 1, i.e m1 ⋅ m2 = -1

CALCULATION:

Given: Equation of lines is 4x – 3y + 6 = 0

The given equation can be re-written as: 

By comparing the above equation with y = m ⋅ x + c we get slope of the given line 

Option A: 3x + 4y - 7 = 0

If equation of the normal is 3x + 4y - 7 = 0 and this equation can be re-written as: 

By comparing the above equation with y = m ⋅ x + c we get slope of the normal 

∵ The line and normal are perpendicular to each other so the product of their slopes should be - 1.

⇒ m₁ ⋅ m₂ = 4/3 ⋅ (- 3/4) = - 1

So, option A represents the equation of the normal to the given.

Hence, option A is the correct answer.