Answer:
C
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 = - 4x + 9 ← 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
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-4}[/tex] = [tex]\frac{1}{4}[/tex], hence
y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation of the perpendicular line
To find c substitute (4, 5) into the partial equation
5 = 1 + c ⇒ c = 5 - 1 = 4
y = [tex]\frac{1}{4}[/tex] x + 4 ← equation of perpendicular line → C
