Answer:
The graph in the attached figure
Step-by-step 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
[tex]3x+y=20[/tex]
Isolate the variable y
[tex]y=-3x+20[/tex]
To graph the line find the intercepts
The x-intercept is equal to the point [tex](6.667,0)[/tex] ----> value of x when the value of y is equal to zero
The y-intercept is equal to the point [tex](0,20)[/tex] ----> 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 [tex]x=0[/tex] ------> [tex]y=-3(0)+20=20[/tex]
For [tex]x=1[/tex] ------> [tex]y=-3(1)+20=17[/tex]
For [tex]x=2[/tex] ------> [tex]y=-3(2)+20=14[/tex]
For [tex]x=3[/tex] ------> [tex]y=-3(3)+20=11[/tex]
For [tex]x=4[/tex] ------> [tex]y=-3(4)+20=8[/tex]
For [tex]x=5[/tex] ------> [tex]y=-3(5)+20=5[/tex]
For [tex]x=6[/tex] ------> [tex]y=-3(6)+20=2[/tex]
The domain (number of fancy goldfish) is the interval---------> [tex][0,1,2,3,4,5,6][/tex]
The range (number of common goldfish) is the interval---------> [tex][20,17,14,11,8,5,2][/tex]
