Answer:
D
Step-by-step explanation:
Firstly, perpendicular line has a slope that is "negative reciprocal" of the given line's slope.
The equation of a line is y = mx + b
Where m is the slope and b is the y-intercept
So, the given line has a slope of "-4", hence the perpendicular line would have a slope of "1/4". So immediately we can eliminate Answer Choice "A".
Now, let's see which of the other choices is our correct answer. Since we know this line has slope of "1/4", we can write:
y = (1/4)x + b
Given the point (4,5), we can replace "x" with "4" and "y" with 5 and find b:
[tex]y=\frac{1}{4}x+b\\5=\frac{1}{4}(4)+b\\5=1+b\\b=5-1\\b=4[/tex]
So, the equation is:
[tex]y=\frac{1}{4}x+4[/tex]
Correct answer is D
