We are asked to sketch the graphs of the linear inequalities 1) $y \ge \frac{1}{4}x - 3$ 2) $y < 5x + 5$ 3) $5x + 2y > -4$ 4) $x + y < 1$

1. Problem Description

We are asked to sketch the graphs of the linear inequalities

1) $y \ge \frac{1}{4}x - 3$

2) $y < 5x + 5$

3) $5x + 2y > -4$

4) $x + y < 1$

2. Solution Steps

1) $y \ge \frac{1}{4}x - 3$

First, we graph the line $y = \frac{1}{4}x - 3$. This line has a y-intercept of -3 and a slope of $\frac{1}{4}$. Since the inequality is $y \ge \frac{1}{4}x - 3$, we draw a solid line and shade the region above the line.

2) $y < 5x + 5$

First, we graph the line $y = 5x + 5$. This line has a y-intercept of 5 and a slope of

5. Since the inequality is $y < 5x + 5$, we draw a dashed line and shade the region below the line.

3) $5x + 2y > -4$

We can rewrite this inequality as $2y > -5x - 4$, or $y > -\frac{5}{2}x - 2$.

First, we graph the line $y = -\frac{5}{2}x - 2$. This line has a y-intercept of -2 and a slope of $-\frac{5}{2}$. Since the inequality is $y > -\frac{5}{2}x - 2$, we draw a dashed line and shade the region above the line.

4) $x + y < 1$

We can rewrite this inequality as $y < -x + 1$.

First, we graph the line $y = -x + 1$. This line has a y-intercept of 1 and a slope of -

1. Since the inequality is $y < -x + 1$, we draw a dashed line and shade the region below the line.

3. Final Answer

The graphs of the inequalities are described in the solution steps and should be drawn on the provided coordinate planes.