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3x+4y=8 slope of a perpenciulare lines

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4 Answers

Hi Young Friend,
I show you another way for finding slop. If you have Ax+By+C=o that it is one of standard form for line.
It is enough, you find -A/B because it is slop.
 
3x+4y=8  3x +4y-8=0   slop = -3/4   as you know A=3 , B=4 . Now if you need slop for perpendicular line is
+4/3 and slop for parallel line is  -3/4. In fact when two lines are parallel they have the same slop. I hope this explain is useful for you. Please feel free if you have any question.
 
Be successful,
Minoo
Hi Aaron;
The equation is currently in standard form...
Ax+By=C, A and B do not equal zero, and A is greater than zero.
The equation must be converted into slope-intercept form...
y=mx+b, m is the slope and b is the y-intercept, the value of y when x=0.
3x+4y=8
4y=-3x+8
y=[(-3/4)x]+2
The slope is -3/4.  The slope of the line perpendicular to such is positive 4/3.
Dear Aaron,
 
3x + 4y = 8
 
4y = 8 - 3x
 
y = 2 - (3/4)x
 
So the slope of the given line is -(3/4).
 
The slope of any and all lines perpendicular to the given line is
 
-[1/(-3/4)] = 4/3
 
The slope of a line that is perpendicular to another line that has slope m is always -(1/m).
 
Take it to the bank.

Comments

Hi Aaron;
I do not know what William is taking to the bank.   But I have done some research, and Touba is correct.  William and I had one oversight.  When an equation is in standard form, as is this one, there is an easier technique to calculate slope.  Slope is -A/B for an equation in the form of Ax+By=C.  The slope of the line perpendicular to it is B/A.  The bank will recognize that as legal tender.

Comment

Two lines are perpendicular if and only if their slopes are opposite reciprocals.
So if one line has a slope of 3/2, a line perpendicular to it must have a slope of -2/3
Or if one line has a slope of 5, a line perpendicular to it must have the slope -1/5
 
First rewrite you equation in slope-intercept form; that is one way to identify the slope. Then find its opposite reciprocal.