Find the value of the constant of proportionality (k)

Question

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

Answer 1

When \( y \) varies directly with \( x \), it can be expressed with the equation:

\[ y = kx \]

where \( k \) is the constant of proportionality. You are provided with \( y = 35 \) when \( x = 5 \). We can substitute these values into the equation to find \( k \).

\[ 35 = k \cdot 5 \]

To solve for \( k \), divide both sides by 5:

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

Calculating this gives:

\[ k = 7 \]

Thus, the constant of proportionality \( k \) is \( \boxed{7} \).