We have to complete the table so that there is a proportional relationship between the number of apples and the weight.
The only complete row we have is 5 apples has a weight of 0.6 kg. So the constant of proportionality is:
[tex]\begin{gathered} \text{We call k the constant of proportionality:} \\ k=\frac{0.6}{5}=0.12\frac{\operatorname{kg}}{apple} \end{gathered}[/tex]
Now, we can write the equation for the relationship:
[tex]\begin{gathered} x=\text{number of apples} \\ y=\text{weight in kilograms } \\ y=k\cdot x \\ \text{Note that k is the constant of proportionality} \end{gathered}[/tex]
Now, we can complete the table:
[tex]\begin{gathered} \text{For x=}2\text{ apples:} \\ y=0.12\cdot2=0.24\operatorname{kg} \\ \text{For y=}1.44\operatorname{kg}\colon \\ 1.44=0.12\cdot x\Rightarrow x=\frac{1.44}{0.12}=12\text{ apples} \\ For\text{ x=1 apple:} \\ y=0.12\cdot1=0.12\operatorname{kg} \end{gathered}[/tex]
