Question

Determine whether y varies directly with x. If so, find the constant of variation and write the equation.

Answer 1

ANSWER

$yes \: \: k = \frac{1}{3} \: \: \: y = \frac{1}{3} x$

EXPLANATION

The given line passes through the origin, hence it has equation of the form,

$y = kx$

Therefore y varies directly as x.

The line passes through the point (3,1)

This implies that,

$1= k(3)$

$k= \frac{1}{3}$

Hence the constant of variation is

$\frac{1}{3}$

The equation is

$y = \frac{1}{3} x$