1. The problem is to graph the linear function $$y = -\frac{1}{4}x + \frac{1}{2}$$ by plotting its intercepts. 2. To find the y-intercept, set $$x = 0$$: $$y = -\frac{1}{4}(0) + \frac{1}{2} = \frac{1}{2}$$ So the y-intercept is at the point $$(0, \frac{1}{2})$$. 3. To find the x-intercept, set $$y = 0$$ and solve for $$x$$: $$0 = -\frac{1}{4}x + \frac{1}{2}$$ Add $$\frac{1}{4}x$$ to both sides: $$\frac{1}{4}x = \frac{1}{2}$$ Multiply both sides by 4: $$x = 2$$ So the x-intercept is at the point $$(2, 0)$$. 4. Plot the points $$(0, \frac{1}{2})$$ and $$(2, 0)$$ on the coordinate plane. 5. Draw a straight line through these two points to graph the function. The final graph shows the line crossing the y-axis at $$\frac{1}{2}$$ and the x-axis at 2, with a negative slope of $$-\frac{1}{4}$$ indicating the line falls as $$x$$ increases.