Question

identify an equation in point-slope intercept form for the line perpendicular to y=3x+5 that passes through (4,-1)

Answer 1

y + 1 = -
`(1)/(3)`(x - 4)

Explanation:

The equation of a line in slope- intercept form is

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

y = 3x + 5 is in this form

with slope m = 3

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

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

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 (a, b) = (4, - 1), thus

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

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