The equation of the line perpendicular to the line 2x - 3y + 5 = 0 and making an intercept 3 with y-axis is

Question

The equation of the line perpendicular to the line 2x - 3y + 5 = 0 and making an intercept 3 with y-axis is (A) 3x + 2y - 6 = 0 (B) 3x + 2y- 12 = 0 (C) 3x - 2y - 6 = 0 (D) 3x + 2y + 6 = 0

Tardigrade Admin · Accepted Answer

The slope of the given line is (2/3). ∴ The slope of the perpendicular to the given line is m=-(3/2). Also, line intercept y -axis =3, i.e., c=3 ∵ y=m x+c ∴ y=-(3/2) x+3 ⇒ 3 x+2 y-6=0

Q. The equation of the line perpendicular to the line $2 x - 3 y + 5 = 0$ and making an intercept $3$ with $y$ -axis is

3x + 2y - 6 = 0

3x + 2y- 12 = 0

3x - 2y - 6 = 0

3x + 2y + 6 = 0

3x + 2y - 5 = 0

The slope of the given line is $\frac{2}{3}$ .
$∴$ The slope of the perpendicular to the given line is $m = - \frac{3}{2}$ .
Also, line intercept $y$ -axis $= 3$ , i.e., $c = 3$
$∵ y = m x + c$
$∴ y = - \frac{3}{2} x + 3$
$\Rightarrow 3 x + 2 y - 6 = 0$

Q. The equation of the line perpendicular to the line 2x−3y+5=0 and making an intercept 3 with y-axis is