Answer:
1) The graph labeled and the ordered pairs plotted are shown in the second picture.
2) To calculate the amount of meat (in pounds) needed for a party of 75 people:
Substitute the value of the Constant of proportionality and [tex]x=75[/tex] into the equation [tex]y=kx[/tex] and then evaluate (The result is 30 pounds).
Step-by-step explanation:
The missing graph is attached.
Proportional relationships have the following form:
[tex]y=kx[/tex]
Where "k" is the Constant of proportionality.
1) You can observe in the graph shown in the first picture this point:
[tex](10,4)[/tex]
So you can subsitute the coordinates of this point into [tex]y=kx[/tex] and solve for "k":
[tex]4=k(10)\\\\k=\frac{4}{10}\\\\k=\frac{2}{5}[/tex]
Now you can find the amount of meat needed for 20, 30, 40, and 50 people with this procedure:
For 20 people
Substituting [tex]k=\frac{2}{5}[/tex] and [tex]x=20[/tex] into the equation [tex]y=kx[/tex] and evaluating, you get:
[tex]y=(\frac{2}{5})(20)=8[/tex]
The ordered pair is:
[tex](20,8)[/tex]
For 30 people
Substituting [tex]k=\frac{2}{5}[/tex] and [tex]x=30[/tex] into the equation [tex]y=kx[/tex] and evaluating, you get:
[tex]y=(\frac{2}{5})(30)=12[/tex]
The ordered pair is:
[tex](30,12)[/tex]
For 40 people
Substituting [tex]k=\frac{2}{5}[/tex] and [tex]x=40[/tex] into the equation [tex]y=kx[/tex] and evaluating, you get:
[tex]y=(\frac{2}{5})(40)=16[/tex]
The ordered pair is:
[tex](40,16)[/tex]
For 50 people
Substituting [tex]k=\frac{2}{5}[/tex] and [tex]x=50[/tex] into the equation [tex]y=kx[/tex] and evaluating, you get:
[tex]y=(\frac{2}{5})(50)=20[/tex]
The ordered pair is:
[tex](50,20)[/tex]
Knowing those values of "y"and having the ordered pairs, you can finish labeling the graph an plotting the ordered pairs (See the second picture.).
2) Substituting [tex]k=\frac{2}{5}[/tex] and [tex]x=75[/tex] into the equation [tex]y=kx[/tex] and evaluating, you can calculate the amount of meat (in pounds) needed for a party of 75 people. This is:
[tex]y=(\frac{2}{5})(75)=30[/tex]
