Linear Equations

Understanding the Problem:

• The slope of a line describes its steepness and direction.
• A negative slope indicates a specific behavior in the line's orientation.

Key Characteristics of a Negative Slope:

• Direction: The line decreases (falls) as it moves from left to right.
• Angle of Inclination (θ): The angle θ (measured from the positive x-axis) is an obtuse angle (90° < θ < 180°).
• Graphical Representation: The line slants downward from upper left to lower right.

Analyzing the Given Options:

• θ is an acute angle: Incorrect (acute angles correspond to positive slopes).
• θ is an obtuse angle: Correct (negative slopes occur when θ is between 90° and 180°).
• Either the line is x-axis or parallel to the x-axis: Incorrect (a line parallel to the x-axis has a slope of 0, not negative).
• None of the above: Incorrect (since the second option is correct).

Conclusion:

If a line has a negative slope, the angle θ it makes with the positive x-axis is an obtuse angle (90° < θ < 180°).