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<span>x² +y² -4x -6y +8=0
(x² -4x) +(y² -6y) = -8
We are going to complete square for x and y,
it should look like a²+2ab+b² = (a +b)², or </span>a²-2ab+b² = (a -b)²,
<span>
(x²-2*2x+2²) -2² + (y²-2*3y +3²)-3²=- 8
(x-2)²+(y-3)²-4-9=-8
</span>(x-2)²+(y-3)²=-8+13
(x-2)²+(y-3)²=5
<span>
Formula a circle (x-h)²+(y-k)²=R², where vertex has coordinates (h, k)
So , for our circle vertex (2,3) and radius = </span>√5<span>
</span>
A) The constant of proportionality in this proportional relationship is 
B) The equation to represent this proportional relationship is y = 0.2x
<h3><u>Solution:</u></h3>
Given that,
The amount Naomi pays each month for international text messages is proportional to the number of international texts she sends that month
Therefore,
This is a direct variation proportion

Let "y" be the amount that Naomi pays each month
Let "x" be the number of international texts she sends that month
Therefore,

y = kx -------- eqn 1
Where, "k" is the constant of proportionality
Thus the constant of proportionality in this proportional relationship is:

<em><u>Last month, she paid $3.20 for 16 international texts</u></em>
Therefore,
y = 3.20
x = 16
Thus from eqn 1,

Substitute k = 0.2 in eqn 1
y = 0.2x
The equation would then be y = 0.2x
-3n+48=0
-3n=-48
-3n/-3 & -48/-3
n=16