Answer:
y varies directly with x
[tex]k = -3[/tex]
The equation is:
[tex]y = -3x[/tex]
Step-by-step explanation:
We can say that and it varies directly with x if it is fulfilled that
[tex]y = kx[/tex]
Where k is a constant known as the constant of variation.
So
[tex]\frac{y}{x} = k[/tex]
This means that if y varies with x then the division of y between x should always be equal to a constant value k.
We must test this for the values shown in the table
[tex]\frac{-3}{1} = -3[/tex]
[tex]\frac{-9}{3} = -3[/tex]
[tex]\frac{-15}{5} = -3[/tex]
The quotient of [tex]\frac{y}{x}[/tex] is always equal to [tex]-3[/tex]. Then [tex]k = -3[/tex] and the variation of y with x is direct
The equation is:
[tex]y = -3x[/tex]
