Math Problem Statement

Which is the graph of the linear inequality y < 3x + 1?

On a coordinate plane, a solid straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the left of the line is shaded. On a coordinate plane, a solid straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the right of the line is shaded. On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the left of the line is shaded. On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the right of the line is shaded.

Solution

The correct graph for the linear inequality y<3x+1y < 3x + 1 is:

On a coordinate plane, a dashed straight line has a positive slope and goes through (-1, -2) and (0, 1). Everything to the left of the line is shaded.

Here's why:

  • Dashed Line: The line is dashed because the inequality is strict ("<") and does not include the line itself.
  • Positive Slope: The line has a positive slope (slope = 3).
  • Shading: Since yy is less than 3x+13x + 1, the region below the line (or to the left when you consider the orientation of the graph) is shaded.

Would you like more details or have any questions?


Here are five related questions:

  1. How would the graph change if the inequality were y3x+1y \leq 3x + 1?
  2. What would the graph look like for the inequality y>3x+1y > 3x + 1?
  3. How do you determine which side of the line to shade for a given inequality?
  4. What is the significance of the slope in the equation y=3x+1y = 3x + 1?
  5. How does changing the y-intercept affect the graph of the inequality?

Tip: When graphing inequalities, always use a dashed line for strict inequalities (like "<" or ">") and a solid line for inclusive inequalities (like "≤" or "≥").

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Math Problem Analysis

Mathematical Concepts

Linear Inequalities
Graphing on Coordinate Plane
Slope of a Line

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9