SOLUTION: what is the equation in standard form of a perpendicular line that's passes through (5,1)._______y+4=-4(x-2)this equation is the beginning problem u use to answer the problem pls h

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Question 989749: what is the equation in standard form of a perpendicular line that's passes through (5,1)._______y+4=-4(x-2)this equation is the beginning problem u use to answer the problem pls help
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
We are asked to write an equation in standard form for line that passes through point (5,1),
and is perpendicular to a line with the equation y%2B4=-4%28x-2%29

The equation of a line can be written in many forms.
Depending on the information given,
we may find it easier to start by writing the equation in one or another form.
Then, if we get the equation of a line in any other form,
we can always find an equivalent equation in standard form.
The standard form of the equation of a line is Ax%2BBy=C ,
with A , B and C being any real numbers,
except that A and B cannot be both zero at the same time.

If we know a point P%28h%2Ck%29 on a line,
and we know that the slope of that line is m ,
we can write an equation for that line in point-slope form as
y-k=m%28x-h%29 .
For example, y%2B4=red%28-4%29%28x-2%29,--->y-%28green%28-4%29%29=red%28-4%29%28x-2%29 is the equation of a line with slope red%28-4%29 that passes through point P%282%2Cgreen%28-4%29%29 .

For perpendicular lines, if they both have slopes,
the product of their slopes is -1 .
That can also be said as "their slopes are negative reciprocals (or opposite reciprocals) of each other."
So for a line has a slope of red%28-4%29,
the slope for any perpendicular line is 1%2F4 .

So we are looking for the equation of a line with slope %281%2F4%29 that passes through point (5,1).
The point-slope form for that line (based on that point) is
y-1=%281%2F4%29%28x-5%29 .
From there, we use what we know of algebra to transform that equation into an equivalent equation in standard form:
y-1=%281%2F4%29%28x-5%29 ---> 4%28y-1%29=%284%29%281%2F4%29%28x-5%29 ---> 4y-4=%281%29%28x-5%29 ---> 4y-4=x-5 ---> -x%2B4y-4=-5 ---> -x%2B4y=-5%2B4
---> highlight%28-x%2B4y=-1%29<--->highlight%28x-4y=1%29 .

NOTE: x-4y=1 is not the only standard form equation for that line.
It may be the simplest or most elegant answer,
although some may like -x%2B4y=-1 , or %281%2F4%29x%2By=1%2F4 ,
but multiplying both sides of the equal sign times any non-zero number gives you an equivalent equation,
so there is an infinite number of equation in standard form for any line.
In our case, multiplying times 1 for example, we get
10x-40y=10 , which is another equivalent equation in standard form.