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 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 is less than , 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:
- How would the graph change if the inequality were ?
- What would the graph look like for the inequality ?
- How do you determine which side of the line to shade for a given inequality?
- What is the significance of the slope in the equation ?
- 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