we are given a proportional relatrelationshipioship and the following statements:
1. 2.5 pounds of peanuts cost $1. To answer this statement we need first to find the equation of the line that models the problem. Since the relationship is proportional the equation is of the form:
[tex]C=mx[/tex]
Now we replace the given point, that is: (7, 17.5), this means that when x = 7, y = 17.5. Replacing we get;
[tex]17.5=m(7)[/tex]
Solving for "m":
[tex]\frac{17.5}{7}=m[/tex][tex]2.5=m[/tex]
Replacing in the equation we get:
[tex]C=2.5x[/tex]
Now we replace the value of x = 2.5 pounds we get:
[tex]\begin{gathered} C=2.5(2.5) \\ C=6.25 \end{gathered}[/tex]
Therefore, 2.5 pounds cost $6.25. The statement is false.
2. 1 pound costs 2.5. replacing x = 1 we get:
[tex]C=2.5(1)=2.5[/tex]
Therefore, 1 pound costs $2.5. the statement is true
3. 5 pounds of peanuts cost 12.5. Replacing x = 5
[tex]C=2.5(5)=12.5[/tex]
Therefore, 5 pounds cost 12.5. The statement is true:
4. 9 pounds cost 19.5. Replacing x = 9, we get
[tex]C=2.5(9)=22.5[/tex]
Therefore, 9 pounds cost 22.5. The statement is false.
5. The point (4,10) is on the graph. To determine this we need to replace x = 4, if we get 10, then the statement is true. Replacing x = 4 we get:
[tex]C=2.5(4)=10[/tex]
Since we got 10, the statement is true.
