Math Problem Statement

Graph the inequality. 2 x minus y less than or equals 8 Question content area bottom left Part 1 Use the graphing tool to graph the inequality.

Solution

Here is the graph of the inequality 2xy82x - y \leq 8 (or equivalently y2x8y \geq 2x - 8):

  • The solid blue line represents the boundary y=2x8y = 2x - 8.
  • The shaded region above the line (in light blue) represents all the points that satisfy the inequality y2x8y \geq 2x - 8.

Would you like more details on how the graph was created, or do you have any questions?

Here are 5 related questions to expand your understanding:

  1. How do you graph inequalities with \leq or \geq?
  2. What does it mean when we shade a region on a graph?
  3. How do you identify which side of the boundary line to shade?
  4. Can an inequality have multiple boundary lines?
  5. How do we graph systems of inequalities?

Tip: Always remember to flip the inequality when multiplying or dividing by a negative number!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Inequalities
Graphing Inequalities

Formulas

Standard form of a linear equation: Ax + By = C
Slope-intercept form: y = mx + b

Theorems

Linear inequality graphing rules
Boundary line theorem for inequalities

Suitable Grade Level

Grades 7-10