Question

FIND THE EQUATION OF STRAIGHT LINE PERPENDICULAR TO THE LINE 3x -4y + 12 =0 AND HAVING SAME y-INTERCEPT AS 2x-y +5 =0.

◆solve with clear steps.

#ch- equation of a straight line.

Answer 1

The y-INTERCEPT of 2x-y=-5 is 5 .
An equation of a line perpendicular to
3x-4y+12=0 is
4x+3y=something
now
4*0 + 3*5=15
so
4x+3y=15

Answer 2

Equation of the given line is 3x – 4y + 11 = 0

Slope of this line y = mx + c

4y = 3x + 11

y = ¾.x + 11/4

m1 = ¾

Let m2 be the slope of the line which is perpendicular to the given  line then

m1m2 = - 1 ( since they are perpendicular )

¾ m2 = - 1

⇒ m2 = - 4/3

Also,  Y-intercept  c = 4/3

Equation of the required line

y = m2x + c

y = - 4/3 x + 4/3

⇒ 3y = - 4x + 4

⇒ 4x + 3y – 4 = 0