Question

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

Explanation:

Step1: Use the point (3,18)

The equation is \( y = kx \). Substitute \( x = 3 \) and \( y = 18 \) into the equation: \( 18 = k \times 3 \).

Step2: Solve for k

To find \( k \), divide both sides of the equation \( 18 = 3k \) by 3: \( k=\frac{18}{3}=6 \). We can also check with the point (5,30): substitute \( x = 5 \) and \( y = 30 \) into \( y = kx \), we get \( 30 = k \times 5 \), then \( k=\frac{30}{5}=6 \). So the constant of variation \( k \) is 6.

Answer:

6