1. The problem is to graph the line given by the equation $$y = -\frac{1}{2}x + 7$$ on a coordinate plane. 2. The equation is in slope-intercept form $$y = mx + b$$ where $$m$$ is the slope and $$b$$ is the y-intercept. 3. Here, the slope $$m = -\frac{1}{2}$$ means the line falls 1 unit vertically for every 2 units it moves horizontally to the right. 4. The y-intercept $$b = 7$$ means the line crosses the y-axis at the point $$(0,7)$$. 5. To graph, start at $$(0,7)$$ on the y-axis. 6. From there, use the slope to find another point: move 2 units right (positive x direction) and 1 unit down (because slope is negative), reaching the point $$(2,6)$$. 7. Plot these two points and draw a straight line through them extending across the coordinate plane. This line will slope downward from left to right, crossing the y-axis at 7 and the x-axis at the point where $$y=0$$. To find the x-intercept, set $$y=0$$: $$0 = -\frac{1}{2}x + 7$$ $$\frac{1}{2}x = 7$$ $$x = \cancel{2} \times 7 = 14$$ So the x-intercept is $$(14,0)$$. The graph passes through points $$(0,7)$$ and $$(14,0)$$ with slope $$-\frac{1}{2}$$.