Math Problem Statement

graph the inequality y>=2x+1

Solution

Here is the graph of the inequality y2x+1y \geq 2x + 1. The shaded area represents the region where yy is greater than or equal to 2x+12x + 1, while the line y=2x+1y = 2x + 1 acts as the boundary.

Would you like further explanation on how to interpret or solve such inequalities?

Here are some related questions for further practice:

  1. How would you graph y3x+2y \leq -3x + 2?
  2. What does it mean when we shade above or below the line in inequalities?
  3. How would the graph change if the inequality were y>2x+1y > 2x + 1 instead?
  4. Can you identify the slope and y-intercept of the line y=2x+1y = 2x + 1?
  5. How do we graph systems of inequalities with more than one constraint?

Tip: When graphing linear inequalities, always check which region satisfies the inequality by testing a point not on the boundary line, like the origin (if it’s not on the line).

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Inequalities
Graphing

Formulas

y = mx + b (Slope-Intercept Form)

Theorems

Slope-Intercept Theorem

Suitable Grade Level

Grades 8-10