Hi Dalia;
3x+2y5=0
We need the equation in the format of y=mx+b for which m=slope, and b is the yintercept, the value of y when x=0.
3x+2y5=0
Let's add 5 to both sides...
5+3x+2y5=0+5
3x+2y=5
Let's subtract 3x from both sides...
3x+3x+2y=3x+5
2y=3x+5
Let's divide both sides by 2...
(2y)/2=[(3x)/2]+(5/2)
y=(3/2)x+(5/2)
The slope of this line is 3/2.
The slope of the line perpendicular to such is positive 2/3.
y=2/3x+b
The yintercept, b, is unknown at this time.
Let's plugin the one coordinate provided to establish such; (2,1).
1=[(2/3)(2)]+b
1=(4/3)+b
Let's subtract 4/3 from both sides...
4/3+1=(4/3)+b(4/3)
1/3=b
y=(2/3)x(1/3)
Nov 21

Vivian L.
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