Question

what is the constant of variation, k, of the line $y = kx$ through $(3, 18)$ and $(5, 30)$?\
\
$\frac{5}{3}$\
\
$\frac{3}{5}$\
\
$6$\
\
$3$

Explanation:

Step1: Recall the formula for constant of variation

For the line \( y = kx \), the constant of variation \( k \) can be found using the formula \( k=\frac{y}{x} \) since \( y = kx \) implies \( k=\frac{y}{x} \).

Step2: Use the point \((3, 18)\) to find \( k \)

Substitute \( x = 3 \) and \( y = 18 \) into the formula \( k=\frac{y}{x} \).
So, \( k=\frac{18}{3}=6 \).

Step3: Verify with the point \((5, 30)\)

Substitute \( x = 5 \) and \( y = 30 \) into the formula \( k=\frac{y}{x} \).
We get \( k=\frac{30}{5}=6 \). Both points give the same value of \( k \), so it is consistent.

Answer:

6