Math Problem Statement
Which of the following statements about the table are true? Select all that apply. Show all work. The table shows a proportional relationship. When x = 20, y is 2.55. All the ratios y/x for related pairs of x and y are equivalent to 8. The unit rate of y/x for related pairs of x and y is 1/8.
Solution
In the question provided, there are several statements about the table, and the instructions are to determine which statements are true based on the table data. Let’s go through each statement one by one, given that we have the data from the table for and values.
Here’s the table data I can see:
\hline x & y \\ \hline 12 & 1.5 \\ 18 & 2.25 \\ 22 & 2.75 \\ 26 & 3.25 \\ \hline \end{array}$$ ### Statement Analysis 1. **The table shows a proportional relationship.** - For a proportional relationship, the ratio $$\frac{y}{x}$$ should be constant across all pairs of $$x$$ and $$y$$. - Let's calculate $$\frac{y}{x}$$ for each pair: - $$\frac{1.5}{12} = 0.125$$ - $$\frac{2.25}{18} = 0.125$$ - $$\frac{2.75}{22} = 0.125$$ - $$\frac{3.25}{26} = 0.125$$ - Since all the ratios are equal, the table indeed shows a proportional relationship. This statement is **true**. 2. **When $$x = 20$$, $$y$$ is 2.55.** - There is no value of $$x = 20$$ in the table, so we cannot directly confirm this from the table. This might involve interpolation, but based on only the given values, this statement cannot be verified as true. So, it’s **false** unless interpolated data is calculated separately. 3. **All the ratios $$\frac{y}{x}$$ for related pairs of $$x$$ and $$y$$ are equivalent to 8.** - From our calculations above, each $$\frac{y}{x}$$ value is 0.125, not 8. Therefore, this statement is **false**. 4. **The unit rate of $$\frac{y}{x}$$ for related pairs of $$x$$ and $$y$$ is $$\frac{1}{8}$$.** - Since $$\frac{y}{x} = 0.125$$ for each pair, and $$0.125 = \frac{1}{8}$$, this statement is **true**. ### Conclusion The statements that are true are: - The table shows a proportional relationship. - The unit rate of $$\frac{y}{x}$$ for related pairs of $$x$$ and $$y$$ is $$\frac{1}{8}$$. Would you like a more detailed explanation of any of these points? --- Here are some follow-up questions that might deepen your understanding: 1. What is a proportional relationship, and how can it be identified from a table of values? 2. How can interpolation be used to estimate values not directly given in the table, like when $$x = 20$$? 3. Why is the unit rate important in understanding proportional relationships? 4. Can you provide an example of a real-life situation that demonstrates a proportional relationship? 5. How would the table look if it did not represent a proportional relationship? **Tip:** To confirm a proportional relationship, always check that the ratio $$\frac{y}{x}$$ remains constant across all pairs.Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Proportional Relationships
Ratios
Unit Rate
Formulas
y/x = constant
Theorems
-
Suitable Grade Level
Grade 7