Question

Write an equation of the line perpendicular to the given line that contains P.

Answer 1

y + 7 = - 3(x - 8)

Explanation:

the equation of a line in slope- intercept form is

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

given the equation

y =
`(1)/(3)` x + 4 ← in slope- intercept form

with slope m =
`(1)/(3)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((1)/(3) )` = - 3

the equation of a line in point- slope form is

y - b = m(x - a)

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

we have nm = - 3 and (a, b ) = P (8, - 7 )

substitute these values into the equation

y - (- 7) = - 3(x - 8) , that is

y + 7 = - 3(x - 8) ← equation of line in point- slope form