Question

what is the constant of variation, k, of the direct variation, $y = kx$, through (5, 8)?
$\bigcirc$ $k = -\frac{8}{5}$
$\bigcirc$ $k = -\frac{5}{8}$
$\bigcirc$ $k = \frac{5}{8}$
$\bigcirc$ $k = \frac{8}{5}$

Explanation:

Step1: Substitute the point into the equation

The direct variation equation is \( y = kx \). We know the point \((5, 8)\) lies on this line, so we substitute \( x = 5 \) and \( y = 8 \) into the equation.
\( 8 = k\times5 \)

Step2: Solve for \( k \)

To find \( k \), we divide both sides of the equation \( 8 = 5k \) by 5.
\( k=\frac{8}{5} \)

Answer:

\( k = \frac{8}{5} \) (corresponding to the option \( k=\frac{8}{5} \))