Question

I need help asap :(​

Answer 1

D

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:

`y=(1)/(4)x+b\\5=(1)/(4)(4)+b\\5=1+b\\b=5-1\\b=4`

So, the equation is:

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

Correct answer is D