Math Problem Statement

What is the slope of the line that passes through the points (-10, -8) and (-9, -8)? Write your answer in simplest form.

Solution

To find the slope of the line that passes through the points (10,8)(-10, -8) and (9,8)(-9, -8), you can use the slope formula:

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

For the given points:

  • (x1,y1)=(10,8)(x_1, y_1) = (-10, -8)
  • (x2,y2)=(9,8)(x_2, y_2) = (-9, -8)

Plugging in the values:

m=8(8)9(10)m = \frac{-8 - (-8)}{-9 - (-10)}

Simplify each part:

  1. In the numerator: 8(8)=8+8=0-8 - (-8) = -8 + 8 = 0
  2. In the denominator: 9(10)=9+10=1-9 - (-10) = -9 + 10 = 1

This gives:

m=01=0m = \frac{0}{1} = 0

So, the slope of the line is 00, which means the line is horizontal.

Would you like further details, or do you have any questions?

Here are five related questions you might explore:

  1. What is the slope of a vertical line?
  2. How do you determine if two points form a horizontal or vertical line?
  3. How can you use the slope to determine if two lines are parallel?
  4. What is the equation of a line with a slope of zero passing through a specific point?
  5. How do you find the slope when given the equation of a line in standard form?

Tip: When the slope calculation results in a zero in the numerator, the line is horizontal, and when the denominator is zero, the slope is undefined (vertical line).

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Math Problem Analysis

Mathematical Concepts

Algebra
Coordinate Geometry
Slope of a Line

Formulas

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

Theorems

Concept of Horizontal and Vertical Lines

Suitable Grade Level

Grade 7-9