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:
$$y = -2.5x + 4.5$$