2. Find the constant of variation k for the inverse variation. Then write an equation for the inverse variation. y = 4.5 when x = 3
a. k = 13.5; xy = 13.5
b. k = 1.5; y = 1.5
x
c. k = 1.5; y = 1.5x
d. k = 13,5; 13.5y = x

Correct choice: a. k = 13.5; xy = 13.5

Step-by-step explanation:

Inverse Proportion

Two variables x and y are in inverse proportion or variation if:

Where k is the constant of proportionality

Since we know that y=4.5 when x=3:

Solving for k:

Thus the equation is:

Or, equivalently:

Correct choice: a. k = 13.5; xy = 13.5

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step-by-step explanation:

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: