Question

Find the equation of the line that is perpendicular to the line Y equals 4X and passes through the point -10, -6. Write the equation in point slope form

Answer 1

y + 6 = -
`(1)/(4)` (x + 10)

Explanation:

the equation of a line in slope- intercept form is

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

y = 4x ← is in slope- intercept form

with slope m = 4

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(4)`

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

here m = -
`(1)/(4)` and (a, b ) = (- 10, - 6 ) , then

y - (- 6) = -
`(1)/(4)` (x - (- 10) ) , that is

y + 6 = -
`(1)/(4)` (x + 10)