Example Card: Graphing a Linear Inequality
Write, solve, and graph inequalities in Grade 9 Algebra. Understand solution sets, open vs. closed circles on number lines, and interval notation. (Saxon Algebra 1, Grade 9)
Key Concepts
Let's turn an inequality into a map of infinite solutions on the coordinate plane. This example focuses on the key idea of graphing a linear inequality.
Example Problem Graph the inequality $y \ge \frac{1}{2}x + 1$.
Step by Step 1. First, graph the boundary line $y = \frac{1}{2}x + 1$. Because the inequality symbol is $\ge$, we will use a solid line . 2. Next, we need to decide which side of the line to shade. We can use an ordered pair as a test point. The point $(0, 0)$ is a good choice since it is not on the line. 3. Substitute the coordinates of the test point into the inequality. $$ y \ge \frac{1}{2}x + 1 $$ $$ 0 \ge \frac{1}{2}(0) + 1 $$ 4. Simplify the expression. $$ 0 \ge 1 $$ 5. This statement is false. The point $(0, 0)$ is not a solution. Therefore, we shade the half plane that does not contain the point $(0, 0)$.
Common Questions
What is Example Card: Graphing a Linear Inequality in Grade 9 Algebra?
Let's turn an inequality into a map of infinite solutions on the coordinate plane Mastering this concept builds a foundation for advanced algebra topics.
How do you approach Example Card: Graphing a Linear Inequality problems step by step?
This example focuses on the key idea of graphing a linear inequality Use this method consistently to avoid common errors.
What is a common mistake when studying Example Card: Graphing a Linear Inequality?
Because the inequality symbol is , we will use a solid line Always check your work by substituting back into the original problem.