Math Problem Statement

Write the inequality shown on each graph (in slope-intercept form).

Solution

The problem asks to write the inequality represented by each graph in slope-intercept form. Let's analyze both graphs based on the image:

  1. Left Graph:

    • The dashed line indicates the boundary of the inequality. Dashed lines suggest the inequality does not include the line itself (i.e., either "<" or ">").
    • The line crosses the y-axis at y=8y = 8 and has a slope of 2-2. This can be verified by noting that the line moves down 2 units for every 1 unit it moves to the right.
    • So, the equation of the line in slope-intercept form is y=2x+8y = -2x + 8.
    • Since the shading is below the line, the inequality will be y<2x+8y < -2x + 8.
  2. Right Graph:

    • The solid line means the inequality includes the boundary line (i.e., either "≤" or "≥").
    • The line crosses the y-axis at y=2y = 2 and has a slope of 22, moving up 2 units for every 1 unit to the right.
    • The equation of the line is y=2x+2y = 2x + 2.
    • Since the shading is above the line, the inequality will be y2x+2y \geq 2x + 2.

Final Inequalities:

  1. Left graph: y<2x+8y < -2x + 8
  2. Right graph: y2x+2y \geq 2x + 2

Let me know if you want further explanation or have questions! Here are some related questions you might find useful:

  1. What is the difference between a dashed and a solid line in graphing inequalities?
  2. How do you find the slope of a line from a graph?
  3. Why does the inequality direction change based on the shading?
  4. Can inequalities have vertical lines, and how would you represent them?
  5. How would these inequalities change if the lines had different slopes?

Tip: Always check the shading and line type (solid or dashed) to correctly interpret inequalities on a graph.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Inequalities
Graphing

Formulas

Slope-intercept form: y = mx + b

Theorems

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Suitable Grade Level

Grades 7-10