Math Problem Statement

solve this and provide the right answers

Find the slope of the line that passes through the pair of points (2, 2) and (-2, -2).

Solution

To find the slope of a line that passes through two points, (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2), we use the slope formula:

slope=m=y2y1x2x1\text{slope} = m = \frac{y_2 - y_1}{x_2 - x_1}

Given points: (x1,y1)=(2,2)and(x2,y2)=(2,2)(x_1, y_1) = (2, 2) \quad \text{and} \quad (x_2, y_2) = (-2, -2)

Now, substitute the values into the slope formula:

m=2222=44=1m = \frac{-2 - 2}{-2 - 2} = \frac{-4}{-4} = 1

Thus, the slope of the line passing through the points (2,2)(2, 2) and (2,2)(-2, -2) is 1\boxed{1}.

Would you like further details or explanations?

Here are five related questions you might want to explore:

  1. What is the slope-intercept form of the line passing through these points?
  2. How do you find the equation of a line using point-slope form?
  3. Can you describe the graphical interpretation of a line with a slope of 1?
  4. What would the slope be if the points were vertically aligned?
  5. How do you determine if two lines are parallel or perpendicular based on their slopes?

Tip: When calculating slope, remember that a positive slope means the line rises as it moves to the right, while a negative slope means the line falls.

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Math Problem Analysis

Mathematical Concepts

Algebra
Coordinate Geometry
Slopes of Lines

Formulas

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

Theorems

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Suitable Grade Level

Grades 6-8