10. \( x+2 y=4 \)

Let's solve the equation \( x + 2y = 4 \) for \( y \). Rearranging gives us \( 2y = 4 - x \), and divising by 2, we find \( y = 2 - \frac{x}{2} \). This is a linear equation, which means it represents a straight line on a graph, where the y-intercept is 2 and the slope is -0.5. Now, if we set \( x = 0 \), then \( y = 2 \); setting \( y = 0 \) would give \( x = 4 \). So, the graph of this equation will cross the y-axis at (0, 2) and the x-axis at (4, 0), creating a visual representation of a line that slopes downward from left to right. Graphing helps visualize linear relationships!