Write an equation for a line perpendicular

I don't understand it. I have the answer, but I don't get it. Could someone please explain ?
Write an equation for a line perpendicular to y=−4x−4 and passing through the point (4,3)
y=
I got 2 for b. y=1/4x+2

You have a line \(\displaystyle 4x+y+4=0\) any line that is perpendicular to that line looks like \(\displaystyle x-4y+C=0\)
How do we find the value of \(\displaystyle C\) if that line is to pass through \(\displaystyle (4,3)~?\)
Well \(\displaystyle x=4~\&~y=3\) so that \(\displaystyle C=-[(4)-4(3)]=8\)
ANS: \(\displaystyle x-4y+8=0\)

At other places in this thread, youhave complained that we have disrespected you for not rememberingbasic pre-calculus. That my friend is unfair of you. Before retiring,I chaired a division of mathematical sciences. As such I caught he**from a new provost about the failure rate in calculus I. So we set aper-calculus test for taking the course. We could not stop anyonefrom taking the course, but we could demand that one failing thepre-test to sine a waiver saying they had been warned. We offered apre-calculus review at no cost. I can tell you that we had greatsuccess by using the very 'quick tricks' I have shown you here. In that term long course the students could become conformable withmathematics.
 
You have a line \(\displaystyle 4x+y+4=0\) any line that is perpendicular to that line looks like \(\displaystyle x-4y+C=0\)
How do we find the value of \(\displaystyle C\) if that line is to pass through \(\displaystyle (4,3)~?\)
Well \(\displaystyle x=4~\&~y=3\) so that \(\displaystyle C=-[(4)-4(3)]=8\)
ANS: \(\displaystyle x-4y+8=0\)

At other places in this thread, youhave complained that we have disrespected you for not rememberingbasic pre-calculus. That my friend is unfair of you. Before retiring,I chaired a division of mathematical sciences. As such I caught he**from a new provost about the failure rate in calculus I. So we set aper-calculus test for taking the course. We could not stop anyonefrom taking the course, but we could demand that one failing thepre-test to sine a waiver saying they had been warned. We offered apre-calculus review at no cost. I can tell you that we had greatsuccess by using the very 'quick tricks' I have shown you here. In that term long course the students could become conformable withmathematics.

At my school you've got to take a pre-calculus placement test and score at least 75% to be allowed to take calculus.
 
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