Math Problem Statement

Find the slope between the points( ) 3, 7 and( ) 8, 3− .

Solution

To find the slope between two points, we use the formula:

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

Where:

  • (x1,y1)(x_1, y_1) are the coordinates of the first point.
  • (x2,y2)(x_2, y_2) are the coordinates of the second point.

In this case, the points are (3,7)(3, 7) and (8,3)(8, -3). So:

  • x1=3,y1=7x_1 = 3, y_1 = 7
  • x2=8,y2=3x_2 = 8, y_2 = -3

Now substitute into the formula:

slope=3783=105=2\text{slope} = \frac{-3 - 7}{8 - 3} = \frac{-10}{5} = -2

The slope between the two points is 2-2.

Would you like further clarification or more details on how the slope formula works?


Related questions:

  1. How do you interpret the slope in terms of the line's steepness?
  2. What happens if the two points have the same x-coordinate?
  3. How do you find the equation of a line given the slope and a point?
  4. How do you calculate the slope between vertical or horizontal lines?
  5. How can the slope formula be applied to determine if two lines are parallel?

Tip: Remember, the slope of a line represents its steepness and direction: a positive slope rises to the right, while a negative slope falls to the right.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Slope of a Line

Formulas

slope = (y2 - y1) / (x2 - x1)

Theorems

Slope formula

Suitable Grade Level

Grades 6-8