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Sagot :
According to the given table.
Days Grams
7 4 1/5
30 18
The constant of proportionality is found with the following formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]First, we transform the mixed number 4 1/5 into a fraction.
[tex]4\frac{1}{5}=\frac{4\cdot5+1}{5}=\frac{20+1}{5}=\frac{21}{5}[/tex]So, we use the following
[tex]\begin{gathered} x_1=7 \\ x_2=30 \\ y_1=\frac{21}{5} \\ y_2=18 \end{gathered}[/tex]Replacing these values in the formula, we have
[tex]m=\frac{18-\frac{21}{5}}{30-7}=\frac{\frac{90-21}{5}}{23}=\frac{\frac{69}{5}}{23}=\frac{69}{23\cdot5}=\frac{69}{115}=\frac{3}{5}[/tex]Therefore, the constant of proportionality is 3/5.
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