Subjects algebra

Graph Classification

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1. The problem asks to classify four graphs into three categories: proportional situation, inversely proportional situation, and other situation. 2. A proportional situation is represented by a straight line passing through the origin with a positive slope, meaning $y \propto x$ or $y = kx$ where $k > 0$. 3. An inversely proportional situation is represented by a curve where $y \propto \frac{1}{x}$, typically a hyperbola, not a straight line. 4. Other situations include linear relationships that do not pass through the origin or non-linear relationships that are not inverse proportional. 5. Graph 1 and Graph 4 are straight lines passing through the origin with positive slope, so they represent proportional situations. 6. Graph 2 is a straight line with a positive y-intercept, not passing through the origin, so it is a linear but not proportional relationship, classified as "Other situation". 7. Graph 3 is a curve starting at the origin and increasing rapidly, representing an exponential or other non-linear increasing relationship, also classified as "Other situation". Final classification: - Situation proportionnelle: Graph 1, Graph 4 - Situation inversement proportionnelle: None of the graphs - Autre situation: Graph 2, Graph 3