Question

3.) What is the constant of proportionality (c.o.p.) in the table below?* number of days food in grams 7 4 30

Answer 1

According to the given table.

Days Grams

7 4 1/5

30 18

The constant of proportionality is found with the following formula.

`m=(y_2-y_1)/(x_2-x_1)`

First, we transform the mixed number 4 1/5 into a fraction.

`4(1)/(5)=(4\cdot5+1)/(5)=(20+1)/(5)=(21)/(5)`

So, we use the following

`\begin{gathered} x_1=7 \\ x_2=30 \\ y_1=(21)/(5) \\ y_2=18 \end{gathered}`

Replacing these values in the formula, we have

`m=(18-(21)/(5))/(30-7)=((90-21)/(5))/(23)=((69)/(5))/(23)=(69)/(23\cdot5)=(69)/(115)=(3)/(5)`

Therefore, the constant of proportionality is 3/5.