Question

Find the equation of the line that passes through (-2,5) and is perpendicular to 2x+2y=18

Answer 1

how to find the equation of a line perpendicular to a line.

Prove that the equation of a line perpendicular to a given line ax + by + c = 0 is bx - ay + λ = 0, where λ is a constant.

Let m11 be the slope of the given line ax + by + c = 0 and m22 be the slope of a line perpendicular to the given line.

Then,

m11 = -abab and m11m22 = -1

⇒ m22 = -1m11m1 = baba

Let c22 be the y-intercept of the required line. Then its equation is

y = m22x + c22

⇒ y = baba x + c22

⇒ bx - ay + ac22 = 0

⇒ bx - ay + λ = 0, where λ = ac22 = constant.

To get it more clear let us assume that ax + by + c = 0 (b ≠ 0) be the equation of the given straight line.

Now convert the ax + by + c = 0 in to slope-intercept form we get,

by = - ax - c

⇒ y = - abab x - cbcb

Therefore, the slope of the straight line ax + by + c = 0 is (- abab).

Let m be the slope of a line which is perpendicular to the line ax + by + c = 0. Then, we must have,

m × (- abab) = - 1

⇒ m = baba

Therefore, the equation of a line perpendicular to the line ax + by + c = 0 is

y = mx + c

⇒ y = baba x + c

⇒ ay = bx + ac

⇒ bx - ay+ k = 0, where k = ac, is an arbitrary constant.

Answer 2

This^ explains what to do to solve this!
Hopefully it helps! :)

Answer 3

so k = ac is the final answer? or bx - ay+ k = 0?

Answer 4

No this is an explanation not the answer.
It is an example

Answer 5

Can you help me solve the problem? Because I get lost every time

Answer 6

Sorry, but I don't know this...well I do but I get lost too
I got this off the internet to maybe it can inform you or help you on how to solve this... :)

Answer 7

ok

Answer 8

Sorry @AlixxKK

Answer 9

it still helped

Answer 10

:) I'm glad it did!