•which of the following equations represents a line that is perpendicular to
y = --4x+9 and passes through the point, (4, 5)?
a. y = -4x+4
b. y = 1/4x+5
c. y = 1/4x+4
d. y = 1/4x+6

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

= - = - = , hence

y = 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 = x + 4 ← equation of perpendicular line → C

4+4+2x

or

2x+8

step-by-step explanation: