The quantities x and y are
proportional
x. y
2. 14
6. 42
11. 77
find the constant of proportionality (r) in the equation
y=rx

r = 7  

Step-by-step explanation:

In a direct proportionality,

y = rx

Substitute a pair of values for x and y

77 = r × 11

Divide each side by 11

r = 77/11 = 7

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: