Slope Calculation Explanation

Problem Statement

  • Given two points:
    • Point 1: $(-13.1, 12.9)$
    • Point 2: $(-12.9, 3.1)$
  • Determine the slope of the line through these points.

Definitions

  • Slope: The slope of a line is a measure of its steepness. It is usually represented by the letter $m$ and is calculated using the formula: m=y<em>2−y</em>1x<em>2−x</em>1m = \frac{y<em>2 - y</em>1}{x<em>2 - x</em>1} Where:
    • $(x1, y1)$ and $(x2, y2)$ are the coordinates of two points on the line.

Calculation of Slope

  1. Assign the points:

    • Let $(x1, y1) = (-13.1, 12.9)$
    • Let $(x2, y2) = (-12.9, 3.1)$

  2. Substitute the coordinates into the slope formula:
    m=3.1−12.9−12.9−(−13.1)m = \frac{3.1 - 12.9}{-12.9 - (-13.1)}

  3. Simplify the numerator and denominator:

    • Numerator: $3.1 - 12.9 = -9.8$
    • Denominator: $-12.9 + 13.1 = 0.2$

  4. Substitute these values back into the equation:
    m=−9.80.2m = \frac{-9.8}{0.2}

  5. Simplifying the fraction:
    m=−49m = -49

Final Outcome

  • Option A stated the slope is $-49$.
  • Option B stated the slope is undefined.
  • In this case, the slope is neither vertical nor does it equal zero, therefore:
    • The correct choice is: A. The slope is -49.