Math Problem Statement

What is the slope of the line that contains the points (-2, 5) and (6, -3)?

Solution

The question asks for the slope of the line that contains the points (2,5)(-2, 5) and (6,3)(6, -3).

Formula for the slope:

m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} where:

  • (x1,y1)=(2,5)(x_1, y_1) = (-2, 5)
  • (x2,y2)=(6,3)(x_2, y_2) = (6, -3)

Substituting the values:

m=356(2)m = \frac{-3 - 5}{6 - (-2)}

Simplify: m=356+2=88=1m = \frac{-3 - 5}{6 + 2} = \frac{-8}{8} = -1

Final Answer:

The slope of the line is: 1\boxed{-1}

Would you like further explanation or have any other questions?

Here are 5 related questions for practice:

  1. How do you find the slope when the two points have the same xx-coordinate?
  2. What is the slope of a horizontal line?
  3. How can the slope formula be used to determine if two lines are parallel?
  4. What does a slope of 0 represent in terms of the line’s direction?
  5. How does the slope of a line relate to its steepness?

Tip: Always carefully subtract the coordinates in the correct order (y2y1) and (x2x1)(y_2 - y_1) \text{ and } (x_2 - x_1) to avoid sign errors.

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Math Problem Analysis

Mathematical Concepts

Algebra
Slope of a Line
Coordinate Geometry

Formulas

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

Theorems

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Suitable Grade Level

Grades 7-9