Question

Find the equation of a straight line perpendicular to the line 3x − 4y + 12 = 0 and having the same y-intercept as 2x − y + 5 = 0.

Answer 1

⇒ Rewriting the given equation 3x − 4y + 12 = 0 into the slope-intercept form, y = mx + c:

−4y = −3x − 12

`y = (-3)/-4 x + 12`

`y = 3/4 x + 12`

∴ `m_1 = 3/4`

⇒ Since the required line is perpendicular, its slope (m₂) is the negative reciprocal,

So, `m_2 = - 1/m_1`

∴ `m_2 = - 4/3`

⇒ Let’s assume x = 0 to find the y-intercept because it is the same as the line 2x − y + 5 = 0:

2(0) − y + 5 = 0

−y = −5

∴ y = 5

So, the y-intercept (c) is 5.

⇒ Using the slope-intercept form y = mx + c with m = `- 4/3` and c = 5:

`y = - 4/3 x + 5`

3y = −4x + 15   ....[Multiplied entire equation by 3.]

4x + 3y − 15 = 0

Hence, the equation of the straight line is 4x + 3y − 15 = 0.