Answer:
y + 1 = - [tex]\frac{1}{3}[/tex](x - 4)
Step-by-step 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
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{3}[/tex]
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) = - [tex]\frac{1}{3}[/tex](x - 4), that is
y + 1 = - [tex]\frac{1}{3}[/tex](x - 4) ← in point- slope form
