Math Problem Statement
The table below shows values that stand in a proportional relationship. Select one value from the table that is equal to the constant of proportionality.
Solution
The table in the image shows values of and that form a proportional relationship. The data given is:
\hline x & y \\ \hline 1 & 3.5 \\ 2 & 7 \\ 4.5 & 15.75 \\ \hline \end{array}$$ In a proportional relationship, the ratio $$\frac{y}{x}$$ remains constant. Let’s check if the ratio is the same for all pairs. For $$x = 1$$ and $$y = 3.5$$: $$\frac{y}{x} = \frac{3.5}{1} = 3.5$$ For $$x = 2$$ and $$y = 7$$: $$\frac{y}{x} = \frac{7}{2} = 3.5$$ For $$x = 4.5$$ and $$y = 15.75$$: $$\frac{y}{x} = \frac{15.75}{4.5} = 3.5$$ Since the ratio $$\frac{y}{x} = 3.5$$ is constant for all the given pairs, this confirms that the relationship is proportional. Would you like more details or have any questions? Here are 5 related questions: 1. How do we determine if a relationship is proportional? 2. Can you explain why the ratio $$\frac{y}{x}$$ is key in proportional relationships? 3. What would happen if one pair in the table had a different ratio? 4. How do you find the constant of proportionality from a table of values? 5. Can proportional relationships be represented as linear equations? **Tip:** To check proportionality, always divide $$y$$ by $$x$$ for each pair of values and verify that the ratio stays the same.Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Proportional Relationships
Ratios
Formulas
y = kx
k = y / x
Theorems
Proportionality Theorem
Suitable Grade Level
Grades 6-8