Question

the value of y varies directly to the value of x. When the value of x is 4, the value of y is -12.
what is the constant variation when y is a function of x, and what is the value of y when x is = -6?
Move the correct answer to each box. Each answer may be used more than once. Not all answers will be used.

the constant of the variation is ____.
the value of y when x is -6 is ____.

Options;
-18
-3
-2
-1/3
1/3
2
3
18

Answer 1

To find the constant of variation, we start with the relationship that \( y \) varies directly with \( x \). This can be expressed as:

\[
y = kx
\]

where \( k \) is the constant of variation.

Given that when \( x = 4 \), \( y = -12 \), we can substitute these values into the equation:

\[
-12 = k(4)
\]

To solve for \( k \), we divide both sides by 4:

\[
k = \frac{-12}{4} = -3
\]

So the constant of variation is **-3**.

Next, we need to find the value of \( y \) when \( x = -6 \). We use the same equation \( y = kx \):

\[
y = -3(-6)
\]

Calculating this gives:

\[
y = 18
\]

Hence, the value of \( y \) when \( x = -6 \) is **18**.

Putting it all together:

The constant of the variation is **-3**.
The value of \( y \) when \( x \) is -6 is **18**.