Question

What is an equation of the line that passes through the point ( 2 , − 3 ) (2,−3) and is perpendicular to the line 2 x + 5 y = 10 2x+5y=10?

Answer 1

Answer: y=-
`(5)/(2)`x+2 or 5x+2y=4

Step-by-step explanation:

let’s make l1: 2x+5y=10,

then 5y=-2x+10

then y=-
`(2)/(5)`x+2

So k1=-
`(2)/(5)`

let’s make the unknown line equals l2: y=k2*x + b

Because l2 is perpendicular to l1, so k2*k1=-1

then who can calculate k2=-
`(5)/(2)`

Because l2 passes the point (2,-3),

so when x=2, we can know y=-3

we can get an equation is -3=-
`(5)/(2)`*2 +b

So b=2

l2: y=-
`(5)/(2)`x +2 or 5x+2y=4