Linear Inequality Graph 3Bfd26

1. **State the problem:** We need to graph the linear inequality $$y < \frac{1}{4}x + 1$$ on a coordinate grid with x- and y-axes ranging from -5 to 5. 2. **Understand the inequality:** The inequality $$y < \frac{1}{4}x + 1$$ means we want to shade the region below the line $$y = \frac{1}{4}x + 1$$. 3. **Graph the boundary line:** - The boundary line is $$y = \frac{1}{4}x + 1$$. - It has slope $$m = \frac{1}{4}$$ and y-intercept $$b = 1$$. - Plot the y-intercept at point $$(0,1)$$. - From $$(0,1)$$, use the slope to find another point: rise 1 unit up for every 4 units right, so from $$(0,1)$$ go right 4 units to $$(4,2)$$. 4. **Draw the boundary line as dashed:** Since the inequality is strict ($$<$), the boundary line should be dashed to indicate points on the line are not included. 5. **Shade the region below the line:** Because the inequality is $$y < \frac{1}{4}x + 1$$, shade the area below the dashed line. 6. **Check a test point:** Use $$(0,0)$$ to verify shading. - Substitute into inequality: $$0 < \frac{1}{4}(0) + 1 \Rightarrow 0 < 1$$ which is true. - So, shade the region containing $$(0,0)$$, which is below the line. **Final answer:** The graph shows a dashed line with slope $$\frac{1}{4}$$ and y-intercept $$1$$, with the region below the line shaded.