Question

In which of the following $x$ and $y$ vary directly with each other. For each direct variation, what constant of variation.

$x$	$1$	$2$	$3$	$4$
$y$	$-5$	$-10$	$-15$	$-20$

Answer 1

$x$	$1$	$2$	$3$	$4$
$y$	$-5$	$-10$	$-15$	$-20$

As we know $y=kx$ is direct variation

$\frac{y}{x}=k$ Here ${}^{\prime }{k}^{\prime }$ is constant of variation

$i)x=1,y=-5$

$\frac{-5}{1}=k$

$k=-5$

$ii)x=2,y=-10$

$\frac{y}{x}=k$

$\frac{-10}{2}=k$

$k=-5$

$iii)x=3,y=-15$

$\frac{y}{x}=k$

$\frac{-15}{3}=k$

$k=-5$

$iv)x=4,y=-20$

$\frac{y}{x}=k$

$\frac{-20}{4}=k$

$k=-5$

So in all the cases $-5$ is the constant of variation.