Question

More Common Core Tasks related to Ratio and Proportion. Complete the followingfour Questions.1.The table below shows how much Joseph has saved the first two weeks.a.Graph to find the amount he saves after 5 weeks.b.Is this a proportional relationship? Explain why or why not

Answer 1

Answer:

a) Graphing the function we have;

Therefore, the amount he saves after 5 weeks is $120

b) The relationship is not proportional because the corresponding values are not proportional and do not pass through the origin.

Explanation:

Given the data in the table.

We can extrapolate to derive the Amount saved in the following weeks;

$\begin{gathered} 0\rightarrow70 \\ 1\rightarrow80 \\ 2\rightarrow90 \\ 3\rightarrow100 \\ 4\rightarrow110 \\ 5\rightarrow120 \end{gathered}$

Graphing the function we have;

Therefore, the amount he saves after 5 weeks is $120

To determine if the relationship is proportional or not.

For it to the proportional;

$\frac{y_1}{x_1}=\frac{y_2}{x_2}=\frac{y_3}{x_3}$

substituting the values from the table or graph, we have;

$\begin{gathered} \frac{y_1}{x_1}=\frac{80}{1} \\ \frac{y_2}{x_2}=\frac{90}{2} \\ \frac{y_3}{x_3}=\frac{100}{3} \\ \frac{80}{1}\ne\frac{90}{2}\ne\frac{100}{3} \end{gathered}$

Therefore, the relationship is not proportional because the corresponding values are not proportional and do not pass through the origin.