Proportional relationships are relationships that can be represented using a uniform or constant rate. The cost of food is not a proportional relationship because it does not use a uniform rate.
The missing table is as follows:
[tex]\begin{array}{cc}Bag&Cost\\0&0\\5&17.5&30&89\end{array}[/tex]
Let:
[tex]x \to[/tex] Bag
[tex]y \to[/tex] Cost
First, we calculate the slope (m) of the table using:
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (5,17.5)[/tex]
The slope (m) is as follows:
[tex]m=\frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m=\frac{17.5 - 0}{5-0}[/tex]
[tex]m=\frac{17.5}{5}[/tex]
[tex]m=3.5[/tex]
Also, calculate the slope (m) using the following points
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (30,89)[/tex]
The slope (m) is as follows:
[tex]m=\frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{89 - 0}{30 - 0}[/tex]
[tex]m = \frac{89}{30}[/tex]
[tex]m = 2.97[/tex]
The calculated slopes are not the same. i.e.
[tex]3.5 \ne 2.97[/tex]
Hence, the cost of food is not a proportional relationship because it does not use a uniform rate.
Read more about proportional relationships at:
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