Answer:
3 cups of peanuts → 8 cups of chocolate chips
15 cups of peanuts → 40 cups of chocolate chips
[tex]y=\dfrac{8}{3}x[/tex]
Step-by-step explanation:
A proportional relationship is one in which two quantities vary directly with each other:
[tex]\boxed{\begin{array}{c}\underline{\textsf{Proportional Relationship}}\\\\\Large\text{$y=kx$}\\\\\textsf{where $k$ is the constant of proportionality}\end{array}}[/tex]
Let the number of cups of peanuts be the independent variable (x) and the number of cups of chocolate chips be the dependent variable (y).
To find the equation that describes the given proportional relationship, we can substitute the one given (x, y) point from the table (6, 16) into y = kx and solve for k:
[tex]16=6 \cdot k\\\\\\k=\dfrac{16}{6}\\\\\\k=\dfrac{8}{3}[/tex]
The equation that describes the proportional relationship is:
[tex]\Large\boxed{\boxed{y=\dfrac{8}{3}x}}\phantom{v}[/tex]
where x is the number of cups of peanuts and y is the number of cups of chocolate chips needed to make a trail mix snack.
To complete the table, substitute x = 3 and x = 15 into the equation of the line:
[tex]x=3\implies y=\dfrac{8}{3}(3)=8[/tex]
[tex]x=15\implies y=\dfrac{8}{3}(15)=40[/tex]
The completed table is attached.
