Algebra 1 test prep: Graphing linear inequalities sample problems

📚 Quick Study Guide

• 📈 Linear Inequality: An inequality involving linear expressions. Its graph is a region bounded by a line.
• ✏️ Standard Form: A linear inequality can be written in the form $Ax + By < C$, $Ax + By > C$, $Ax + By \leq C$, or $Ax + By \geq C$.
• 🧭 Graphing Steps:
  1. Rewrite the inequality as an equation and graph the corresponding line. Use a dashed line for $<$ or $>$, and a solid line for $\leq$ or $\geq$.
  2. Choose a test point (not on the line) and substitute its coordinates into the original inequality.
  3. If the test point satisfies the inequality, shade the region containing the test point. Otherwise, shade the other region.
• 🧪 Test Point: The point $(0,0)$ is often a good choice as a test point, unless the line passes through the origin.

Practice Quiz

1. Which inequality is represented by the graph with a dashed line and shading above?
   1. $y > x + 2$
   2. $y < x + 2$
   3. $y \geq x + 2$
   4. $y \leq x + 2$
2. Which point satisfies the inequality $2x - y > 4$?
   1. (0, 0)
   2. (1, -3)
   3. (2, 0)
   4. (0, -4)
3. What is the slope of the boundary line for the inequality $3x + 4y \leq 12$?
   1. $\frac{3}{4}$
   2. $-\frac{3}{4}$
   3. $\frac{4}{3}$
   4. $-\frac{4}{3}$
4. Which inequality has a solid boundary line?
   1. $y > 2x - 1$
   2. $y < 2x - 1$
   3. $y \neq 2x - 1$
   4. $y \geq 2x - 1$
5. What region is shaded for $y \leq -x + 5$?
   1. Above the line
   2. Below the line
   3. To the right of the line
   4. To the left of the line
6. If the test point (0,0) satisfies the inequality, which side of the line do you shade?
   1. The side containing (0,0)
   2. The side not containing (0,0)
   3. It doesn't matter which side
   4. Only shade the line
7. Which inequality represents a horizontal line?
   1. $x > 3$
   2. $y > 3x$
   3. $y > 3$
   4. $x + y > 3$