Question

Write an equation of the line passing through point p (2,3) that is perpendicular to the line y-4 = -2(x+3)

Answer 1

y - 3 =
`(1)/(2)`(x - 2)

Explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 4 = - 2(x + 3) ← is in point- slope form

with slope m = - 2

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-2)` =
`(1)/(2)`

passing through (2, 3 ), then

y - 3 =
`(1)/(2)`(x - 2) ← equation of perpendicular line