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

The direct variation equation can be given as:

`y=6x`

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.