Question

determine whether y varies directly with x. if so, find the constant of variation and write the equation.​

Answer 1

For this case we have that if and it varies directly with x, we can write the equation as:

$y = kx$

Where:

k: It is the constant of proportionality.

According to the table:

$-3 = k (1)$

Clearing k:

$k = -3$

Then,$y = -3x$

Answer:

Option C

Answer 2

Answer:

y varies directly with x

$k = -3$

The equation is:

$y = -3x$

Step-by-step explanation:

We can say that and it varies directly with x if it is fulfilled that

$y = kx$

Where k is a constant known as the constant of variation.

So

$\frac{y}{x} = k$

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

$\frac{-3}{1} = -3$

$\frac{-9}{3} = -3$

$\frac{-15}{5} = -3$

The quotient of $\frac{y}{x}$ is always equal to $-3$. Then $k = -3$ and the variation of y with x is direct

The equation is:

$y = -3x$