Question

What is the constant of variation, k, of the direct variation, y = for, through (5,8)?

Answer 1

Answer:

$\frac{8}{5}$

Step-by-step explanation:

The constant of direction variation givens a proportion that is maintained by both x and y values for all points of a line that it passes through.

Usually represented with the variable $k$, it is given by:

$\frac{y}{x}=k$ for coordinates (x, y).

This relationship can be written as $y=kx$ which is also the layout for a proportional relationship.

Since coordinates are written (x, y), for point (5, 8), substitute $x=5, y=8$ to get the constant of variation:

$8=5k,\\k=\boxed{\frac{8}{5}}$

Answer 2

Answer:

8/5

Step-by-step explanation:

Given that y varies directly with x , therefore ,

$\implies y \propto x$

Let k be the constant . Therefore ,

$\implies y = k x$

When the point is (5,8) ,

$\implies 8 = k * 5 \\\\\implies \underline{\underline{\boxed{ k =\dfrac{8}{5}}}}$

Hence the constant of variation is 8/5.