For each line, determine whether the slope is positive, negative, zero, or undefined.
Understand the Problem
The question asks us to determine the slope of each of the four lines. The slope can be positive, negative, zero, or undefined depending on the line's orientation.
Answer
Line 1: Undefined Line 2: Zero Line 3: Positive Line 4: Negative
Answer for screen readers
Line 1: Undefined Line 2: Zero Line 3: Positive Line 4: Negative
Steps to Solve
- Analyze Line 1
Line 1 is a vertical line. The slope of a vertical line is undefined because the change in $x$ is zero, leading to division by zero in the slope formula: $m = \frac{\Delta y}{\Delta x} = \frac{\Delta y}{0}$, which is undefined.
- Analyze Line 2
Line 2 is a horizontal line. The slope of a horizontal line is zero because the change in $y$ is zero. Using the slope formula: $m = \frac{\Delta y}{\Delta x} = \frac{0}{\Delta x} = 0$.
- Analyze Line 3
Line 3 rises from left to right. This means that as $x$ increases, $y$ also increases. Therefore, the slope is positive, $m > 0$.
- Analyze Line 4
Line 4 falls from left to right. This means that as $x$ increases, $y$ decreases. Therefore, the slope is negative, $m < 0$.
Line 1: Undefined Line 2: Zero Line 3: Positive Line 4: Negative
More Information
The slope of a line is a measure of its steepness and direction. It can be positive, negative, zero, or undefined. A positive slope indicates an increasing line, a negative slope indicates a decreasing line, a zero slope indicates a horizontal line, and an undefined slope indicates a vertical line.
Tips
A common mistake is confusing zero slope with undefined slope. Horizontal lines have zero slope, while vertical lines have undefined slopes. Also, forgetting that slope is calculated as "rise over run" $ (\frac{\Delta y}{\Delta x}) $ is a common mistake.
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