Graphing Inequalities
Graph linear inequalities in one or two variables in Grade 9 algebra: represent one-variable solutions on a number line, and two-variable inequalities as shaded half-planes on the coordinate plane.
Key Concepts
New Concept A linear inequality in one variable is an inequality that can be written as $ax < b$, $ax b$, $ax \le b$, $ax \ge b$, or $ax \neq b$, where $a$ and $b$ are real numbers. What’s next This is your introduction to inequalities. Soon, we'll dive into worked examples on graphing solutions and writing inequalities from visual representations.
Common Questions
How do you graph a linear inequality in one variable?
Solve the inequality for the variable. Mark the boundary point on a number line (open circle for < or >, closed for ≤ or ≥). Shade the ray in the direction satisfying the inequality. For x > 3: open circle at 3, shade to the right.
How do you graph a two-variable linear inequality like y ≤ 2x - 1?
Graph the boundary line y = 2x - 1 as a solid line (since ≤ includes equality). Pick a test point such as (0,0): 0 ≤ 2(0)-1 → 0 ≤ -1 is false. Shade the opposite side from the test point — shade below the line.
What is the standard form of a linear inequality in one variable?
Standard forms are ax < b, ax > b, ax ≤ b, or ax ≥ b where a and b are real numbers. Solving proceeds exactly like a linear equation, except the direction of the inequality flips when multiplying or dividing by a negative number.