1. The problem is to construct functions that model linear relationships. 2. A linear function has the form $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. The slope $m$ represents the rate of change of $y$ with respect to $x$. 4. The y-intercept $b$ is the value of $y$ when $x=0$. 5. To construct a linear function, identify the slope and y-intercept from the problem context. 6. For example, if a problem states that for every 1 unit increase in $x$, $y$ increases by 3 units and when $x=0$, $y=2$, then the function is $$y = 3x + 2$$. 7. Always check the units and context to ensure the function models the relationship correctly. 8. This function can be used to predict $y$ for any value of $x$ within the domain. Final answer: The general form of a linear function modeling a linear relationship is $$y = mx + b$$ where $m$ and $b$ are determined by the problem's conditions.