Subjects algebra

Line Curve

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Line Curve


1. The problem is to identify and analyze the graph of a function described with points and behavior. 2. The graph passes through the point (1, 2). This means that the function's value at $x=1$ is $2$, so $f(1)=2$. 3. The graph slopes downwards crossing the y-axis slightly above $y=4$. This means the y-intercept $f(0)$ is slightly greater than $4$. 4. Given these properties, a possible function could be a linear or a simple polynomial function with negative slope. 5. To model this curve simply, consider a linear function $y = mx + b$. Using $(1,2)$ and y-intercept slightly above 4, suppose $b=4.5$ (since slightly above 4). 6. Calculate slope $m$ using the points $(0,4.5)$ and $(1,2)$: $$m = \frac{2 - 4.5}{1 - 0} = \frac{-2.5}{1} = -2.5$$ 7. Thus the function is: $$y = -2.5x + 4.5$$ 8. This function matches the description: passes through $(1,2)$, crosses y-axis at 4.5, and slopes downward. Final answer: $$y = -2.5x + 4.5$$