Question

wavelength varies inversely with frequency.
let ( x = ) wavelength and ( y = ) frequency.

visible light	wavelength (( m ))	frequency (thz)	( k )
green	520	580	301,600
yellow	560	540	302,400
red	635	480	304,800

the equation that models the relationship between the wavelength and frequency of yellow light is:

Explanation:

Step1: Recall inverse variation formula

For inverse variation, the formula is \( xy = k \) (or \( y=\frac{k}{x} \)), where \( x \) and \( y \) are the two variables, and \( k \) is the constant of variation.

Step2: Identify values for yellow light

For yellow light, \( x = 560 \) (wavelength in m) and \( k = 302400 \) (from the table). Using the inverse variation formula \( xy = k \), we can write the equation as \( x \times y=302400 \) or \( y = \frac{302400}{x} \). Alternatively, substituting \( x = 560 \) and \( y = 540 \), we check \( 560\times540 = 302400 \), which matches the \( k \) value. So the equation modeling the relationship for yellow light is \( xy=302400 \) (or \( y=\frac{302400}{x} \)).

Answer:

\( xy = 302400 \) (or \( y=\frac{302400}{x} \))