1. **Problem Statement:** We are given a graph with multiple parallel diagonal lines with positive slopes and different intercepts. We need to find the linear equation $g(x,y)$ representing the level set of these lines. 2. **Understanding the Problem:** Each line is of the form $$y = mx + c$$ where $m$ is the slope and $c$ is the y-intercept. 3. **Observations:** The lines are parallel, so they share the same slope $m$. The lines are evenly spaced diagonally, indicating a constant difference in intercepts. 4. **Finding the Slope $m$:** From the description, the lines have positive slopes. Since the lines are diagonal and parallel, let's assume the slope $m$ is constant. The grid shows x-values from approximately $-3$ to $3$ and y-values from approximately $-5$ to $5$. The slope can be approximated by the ratio of vertical change to horizontal change between points on a line. 5. **Formulating the Level Set Equation:** A level set for a function $g(x,y)$ is a set of points $(x,y)$ where $g(x,y) = k$ for some constant $k$. For linear functions, this can be written as: $$g(x,y) = ax + by = k$$ where $a$ and $b$ are constants related to the slope. 6. **Relating to the Line Equation:** From $y = mx + c$, rearranged as: $$y - mx = c$$ This can be written as: $$-mx + y = c$$ or equivalently: $$g(x,y) = -mx + y = k$$ where $k = c$ varies for each line. 7. **Conclusion:** The level set function is: $$g(x,y) = -mx + y$$ where $m$ is the slope of the lines. Since the slope is positive and the lines are diagonal, a common slope for such lines is $m=1$ (45 degrees). Thus: $$g(x,y) = -1 \cdot x + y = y - x$$ The level sets are lines where $y - x = k$ for different constants $k$. **Final answer:** $$g(x,y) = y - x$$