Question

Find the value of the constant of proportionality ( k) for the given variation. Find the value of k if y varies directly with x and y+ 35 when x+ 5.

The constant of proportionally k= ___

Answer 1

To find the constant of proportionality \( k \) for the variation where \( y \) varies directly with \( x \), we can use the relationship given by the formula:

\[
y = kx
\]

From the information given, we know:

- When \( x + 5 \), \( y + 35 \).

This can be interpreted as:
- When \( x = 5 \), \( y = 35 \).

We can substitute these values into the direct variation equation to find \( k \).

1. Substitute \( x = 5 \) and \( y = 35 \) into the equation:

\[
35 = k(5)
\]

2. Solve for \( k \):

\[
k = \frac{35}{5} = 7
\]

Thus, the value of the constant of proportionality \( k \) is:

\[
\boxed{7}
\]