Question

Which of the following is the equation of a line perpendicular to the line y =

-10x + 1, passing through the point (5,7)?

Answer 1

y =
`(1)/(10)` x +
`(13)/(2)`

Explanation:

The equation of a line in slope- intercept form is

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

y = - 10x + 1 ← is in slope- intercept form

with slope m = - 10

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-10)` =
`(1)/(10)`, thus

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

To find c substitute (5, 7) into the partial equation

7 =
`(1)/(2)` + c ⇒ c = 7 -
`(1)/(2)` =
`(13)/(2)`

y =
`(1)/(10)` x +
`(13)/(2)` ← equation of line

Answer 2

1/10x - y = -13/2

Explanation: