Question

What is the y-intercept of the equation of the line that is perpendicular to the line y =

x + 10 and passes through the point
(15,-5)?
Ov=x=20
Ov=-*}x+20
v=5x=20
y=-3x +20

Answer 1

`y` intercept
`=10`

line
`y=-x+10`

Explanation:

Let
`y=mx+b` is the required line.

Slope of perpendicular lines : If
`m_(1)` and
`m_(2)` be slope of two perpendicular lines. Them
`m_(1)* m_(2)=-1`

`y=mx+b` is perpendicular to
`y=x+10`

the slope of
`y=x+10` is
`=1`

`m* 1=-1\\m=-1`

Hence eqn is
`y=-x+b`

This equation passes through
`(15,-5)`

`-5=-15+b\\b=-5+15\\b=10`

so the line is
`y=-x+10`

y-intercept :

Substitute
`x=10`

`y=0+10\\y=10`