Question

TheThe equation of the line passing through(2,5) and perpendicular to the line d. 2x-7y=0 can be expressed in the form 7x+ky =b Give only the value of b.

Answer 1

To two lines be perpendicular theirs angular coeficients needs to be the opposite inverse, so, we have the line 2x - 7y = 0 => 7y = 2x => y = 2x/7 it have a 2/7 angular coeficient, so the other line need to be the opposite inverse, and it's -7/2

Let's discover the other line:

(y - yo) = m.(x - xo)

(y - 5) = -7/2.(x - 2)

y - 5 = -7x/2 + 7.2/2

y - 5 = -7x/2 + 7

y = -7x/2 + 7 + 5

y = -7x/2 + 12

Let's multiply all the equation by 2.

2y = -7x + 24

Pass -7x

7x + 2y = 24

7x + ky = b

b is 24 and k is 2