Question

Fancy goldfish x cost $3 each and common goldfish y cost $1 each.

Graph the function y=20-3x to determine how many of each type of goldfish tasha can buy for $20

Answer 1

Fancy. Common
0. 20
1. 17
2. 14
3. 11
4. 8
5. 5
6. 2

Answer 2

The graph in the attached figure

Explanation:

Let

x------> the number of fancy goldfish

y-----> the number of common goldfish

we know that

The linear equation that represent the situation is equal to

`3x+y=20`

Isolate the variable y

`y=-3x+20`

To graph the line find the intercepts

The x-intercept is equal to the point
`(6.667,0)` ----> value of x when the value of y is equal to zero

The y-intercept is equal to the point
`(0,20)` ----> value of y when the value of x is equal to zero

Plot the points

The graph in the attached figure

The solution of the problem is all positive ordered pairs of whole numbers belong to the line

The possible solutions are

For
`x=0` ------>
`y=-3(0)+20=20`

For
`x=1` ------>
`y=-3(1)+20=17`

For
`x=2` ------>
`y=-3(2)+20=14`

For
`x=3` ------>
`y=-3(3)+20=11`

For
`x=4` ------>
`y=-3(4)+20=8`

For
`x=5` ------>
`y=-3(5)+20=5`

For
`x=6` ------>
`y=-3(6)+20=2`

The domain (number of fancy goldfish) is the interval--------->
`[0,1,2,3,4,5,6]`

The range (number of common goldfish) is the interval--------->
`[20,17,14,11,8,5,2]`