Question

PLEASE GIVE ME A REAL ANSWER---------------- Passes through the point (3, 6) and is perpendicular to the line through the points (5, 2) and (6, 21)

Answer 1

x + 19y = 117

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (5, 2) and (x₂, y₂ ) = (6, 21)

m =
`(21-2)/(6-5)` = 19

Given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(19)` , thus

y = -
`(1)/(19)` x + c ← is the partial equation

To find c substitute (3, 6) into the partial equation

6 = -
`(3)/(19)` + c ⇒ c = 6 +
`(3)/(19)` =
`(117)/(19)`

y = -
`(1)/(19)` x +
`(117)/(19)` ← equation in slope- intercept form

Multiply through by 19

19y = - x + 117 ( add x to both sides )

x + 19y = 117 ← equation in standard form

Answer 2

hope that helps that is the answer I have gotten