Math Problem Statement

for 11 12 13 and 14 Next 4 answers should be in the form of y first...then the inequality sign...then the rest of the answer in slope intercept form

For 11, 12, 13, and 14, provide inequalities with y first, then the inequality sign, then the rest in slope-intercept form.

Solution

Here are the inequalities for each graph in the form you requested, with yy first:

11.

The line has a negative slope and the shading is below the line: y<x2y < -x - 2

12.

The line has a positive slope and the shading is above the line: y>12x1y > \frac{1}{2}x - 1

13.

The line has a positive slope, and the shading is above the dashed line: y>x+2y > x + 2

14.

The line has a negative slope and the shading is below the line: y<12x+3y < -\frac{1}{2}x + 3

Would you like any further explanations on how these inequalities were derived, or details on the graph interpretations?

Here are 5 related questions that expand on this topic:

  1. How do you determine the slope of a line from a graph?
  2. What does a solid line versus a dashed line indicate in an inequality?
  3. How do you decide which side of the line to shade for an inequality?
  4. Can you convert these inequalities into standard form?
  5. How do these inequalities change if the inequality sign is flipped?

Tip: When graphing inequalities, always check if the inequality includes the boundary (solid line for \leq or \geq) or if it excludes the boundary (dashed line for << or >>).

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Math Problem Analysis

Mathematical Concepts

Algebra
Graphing Linear Inequalities
Slope-Intercept Form

Formulas

y = mx + b for slope-intercept form
Slope formula: (change in y) / (change in x)

Theorems

Linear Inequality Theorem

Suitable Grade Level

Grades 9-11