The system of inequalities shown in the images is:

$y \geq -\frac{7}{4}x + 4$ $y < \frac{1}{4}x - 4$

Steps to match the graph:

1. Graph the first inequality: $y \geq -\frac{7}{4}x + 4$

   • The line $y = -\frac{7}{4}x + 4$ has a slope of $-\frac{7}{4}$ and a y-intercept of 4.
   • Since the inequality is $\geq$, the shading should be above the line, and the line should be solid.

2. Graph the second inequality: $y < \frac{1}{4}x - 4$

   • The line $y = \frac{1}{4}x - 4$ has a slope of $\frac{1}{4}$ and a y-intercept of $-4$.
   • Since the inequality is $<$, the shading should be below the line, and the line should be dashed.

Now, to choose the correct graph:

• Look for a graph where one line is solid and has a steep negative slope, and another line is dashed with a gentler positive slope.
• The shading should be above the solid line and below the dashed line.

Based on the description, select the graph that satisfies these conditions.

Do you want more details or have any questions?

Here are 5 related questions:

1. How do you determine which side of a line to shade for an inequality?
2. How do solid and dashed lines differ when graphing inequalities?
3. What is the significance of the slope and y-intercept in graphing a linear equation?
4. How would the graph change if the inequalities were reversed (e.g., $y \leq$ instead of $y \geq$)?
5. What methods can you use to check if a point satisfies both inequalities?

Tip: Always test a point (like $(0, 0)$) to see if it lies in the shaded region!