Math Problem Statement

For each line, determine whether the slope is positive, negative, zero, or undefined.

Solution

To determine the slope for each line, we analyze the direction and angle of each line segment shown. Here’s the breakdown:

  1. Line 1: The line slopes downwards from left to right, indicating a negative slope.
  2. Line 2: The line is horizontal, meaning it has no rise (change in yy) and only runs along xx, giving it a zero slope.
  3. Line 3: The line slopes upwards from left to right, showing a positive slope.
  4. Line 4: The line is vertical, meaning there is no change in xx (only a rise in yy), which results in an undefined slope.

Thus, the answers for each line's slope are:

  • Line 1: Negative
  • Line 2: Zero
  • Line 3: Positive
  • Line 4: Undefined

Would you like further details or have any questions?

Related Questions:

  1. What is the difference between a positive and negative slope?
  2. Why is a vertical line’s slope undefined?
  3. How can you determine the slope of a line given two points on the line?
  4. What is the meaning of a zero slope in a real-world context?
  5. How do slopes relate to the angle a line makes with the x-axis?

Tip:

Remember, the slope is the ratio of the vertical change to the horizontal change. This helps in determining if it’s positive, negative, zero, or undefined.

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Math Problem Analysis

Mathematical Concepts

Slope
Graphing Lines

Formulas

Slope formula: m = (y2 - y1) / (x2 - x1)

Theorems

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Suitable Grade Level

Grades 6-8