Question

1. graph: $y < x + 4$ and $y \geq -x + 1$

Explanation:

Step1: Graph boundary $y=x+4$

This is a line with slope $1$, y-intercept $(0,4)$. Use a dashed line (since inequality is $<$).

Step2: Shade region for $y < x+4$

Shade all area below the dashed line (since $y$ is less than the line's value).

Step3: Graph boundary $y=-x+1$

This is a line with slope $-1$, y-intercept $(0,1)$. Use a solid line (since inequality is $\geq$).

Step4: Shade region for $y \geq -x+1$

Shade all area above the solid line (since $y$ is greater than/equal to the line's value).

Step5: Identify overlapping region

The solution is the area shaded by both steps 2 and 4.

Answer:

The graph consists of:

1. A dashed line $y = x + 4$, with shading below the line.
2. A solid line $y = -x + 1$, with shading above the line.
3. The overlapping shaded area (where both conditions are satisfied) is the solution set.

To plot the lines precisely:

• For $y=x+4$: plot $(0,4)$ and $(1,5)$, draw dashed line through them.
• For $y=-x+1$: plot $(0,1)$ and $(1,0)$, draw solid line through them.

The overlapping shaded region is between the two lines, below the dashed line and above the solid line.