Subjects statistics

Action Films 0E01De

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1. **State the problem:** We are given data about students who like action films and need to analyze the relationship between total students and those who like action films. 2. **Complete the table:** The problem states 1 out of 3 students likes action films, so the ratio is $\frac{1}{3}$. We check the table values: | Total Students | Action Film Fans | |----------------|------------------| | 60 | 20 | | 120 | 40 | | 180 | 60 | | 240 | 80 | Each "Action Film Fans" value is exactly $\frac{1}{3}$ of the "Total Students" value, confirming the table is complete and consistent. 3. **Graph the relationship:** Plot points $(60,20)$, $(120,40)$, $(180,60)$, and $(240,80)$ on a coordinate grid with $x$ as total students and $y$ as students who like action films. 4. **Determine proportionality:** Since $y$ is always $\frac{1}{3}x$, the graph is a straight line through the origin, showing a proportional relationship. 5. **Write the equation:** The constant of proportionality is $k=\frac{1}{3}$, so the equation is: $$y=\frac{1}{3}x$$ This means for every 3 students, 1 likes action films. Final answer: The relationship is proportional with equation $y=\frac{1}{3}x$.