4. $y \\geq \\frac{1}{4}x - 5$

Explanation:

Step1: Identify boundary line form

The inequality $y \geq \frac{1}{4}x - 5$ has a boundary line $y = \frac{1}{4}x - 5$, which is in slope-intercept form $y=mx+b$, where $m=\frac{1}{4}$ (slope) and $b=-5$ (y-intercept).

Step2: Plot y-intercept

The y-intercept is $(0, -5)$. Mark this point on the graph.

Step3: Use slope to find second point

Slope $\frac{1}{4}$ means $\frac{\text{rise}}{\text{run}} = \frac{1}{4}$. From $(0, -5)$, move up 1 unit and right 4 units to get the point $(4, -4)$. Mark this point.

Step4: Draw boundary line

Connect $(0, -5)$ and $(4, -4)$ with a solid line (since the inequality is $\geq$, inclusive of the boundary). Extend the line across the grid.

Step5: Shade the solution region

Since the inequality is $y \geq \frac{1}{4}x - 5$, shade the area above the solid boundary line.

Answer:

The graph consists of a solid line $y = \frac{1}{4}x - 5$ (passing through $(0, -5)$ and $(4, -4)$) with the region above this line shaded.