Math Problem Statement
Determine if the table represents a proportional relationship and, if so, find the equation.
Solution
Let's analyze the table to determine if it represents a proportional relationship between and .
Step 1: Check the Ratios
The table shows the following pairs of and values:
x & y \\ \hline 3 & 18 \\ 5 & 30 \\ 7 & 42 \\ 9 & 54 \\ \end{array}$$ To verify if this is a proportional relationship, we calculate the ratio $$\frac{y}{x}$$ for each pair: 1. For $$x = 3$$ and $$y = 18$$: $$\frac{y}{x} = \frac{18}{3} = 6$$ 2. For $$x = 5$$ and $$y = 30$$: $$\frac{y}{x} = \frac{30}{5} = 6$$ 3. For $$x = 7$$ and $$y = 42$$: $$\frac{y}{x} = \frac{42}{7} = 6$$ 4. For $$x = 9$$ and $$y = 54$$: $$\frac{y}{x} = \frac{54}{9} = 6$$ Since all ratios are equal, the relationship between $$x$$ and $$y$$ is indeed proportional, with a constant ratio $$k = 6$$. ### Step 2: Write the Equation Since $$y$$ is proportional to $$x$$, we can write the equation as: $$y = kx$$ Substituting $$k = 6$$: $$y = 6x$$ ### Summary - **Constant of Proportionality ( $$k$$ ):** 6 - **Equation:** $$y = 6x$$ Would you like further details on any part of this solution? ### Further Questions 1. How would you verify a proportional relationship if the values were less straightforward? 2. What happens to the graph of $$y = 6x$$ when we change the constant $$k$$? 3. Can you identify other real-life situations that form a proportional relationship? 4. What would the equation look like if the constant of proportionality were a fraction? 5. How would you determine if a table is not proportional? ### Tip When checking for proportionality, remember that all pairs must have the same ratio for it to be considered proportional.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Proportionality
Ratios
Algebra
Formulas
y = kx
k = y/x
Theorems
Proportional Relationship
Suitable Grade Level
Grades 6-8