Question

At a summer camp there is one counselor for every 6 campers. Write a direct variation equation for the number of campers, y, that there are for x counselors. Then graph.

Answer 1

Answer:

The direct variation equation can be given as:

$y=6x$

Step-by-step explanation:

Given:

At a summer camp there are 6 campers under one counselor.

To find the direct variation equation for the number of campers in terms of number of counselor.

Solution:

$y\rightarrow$ Number of campers

$x\rightarrow$ Number of counselors

We have $y$ ∝ $x$

The direct variation equation can be written as:

$y=kx$

where $k$ is the direct variation constant.

There are 6 campers under one counselor. Using this statement we can find value of $k$

Given: when $x=1$ then $y=6$

We have,

$6=k(1)$

∴ $k=6$

Thus, the direct variation equation can be given as:

$y=6x$

We can find the points using the equation to plot.

$x$              $y=6x$

0                      0

1                       6

2                     12

The graph is sown below.