Math Problem Statement

What is the slope of the line that passes through the points left parenthesis, 7, comma, minus, 6, right parenthesis(7,−6) and left parenthesis, 6, comma, minus, 6, right parenthesis(6,−6)? Write your answer in simplest form.

Solution

To find the slope of the line that passes through the points (7,6)(7, -6) and (6,6)(6, -6), we can again use the slope formula:

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

Where:

  • (x1,y1)=(7,6)(x_1, y_1) = (7, -6)
  • (x2,y2)=(6,6)(x_2, y_2) = (6, -6)

Substituting these values into the formula:

m=6(6)67=6+61=01m = \frac{-6 - (-6)}{6 - 7} = \frac{-6 + 6}{-1} = \frac{0}{-1}

Since the numerator is 0:

m=0m = 0

So, the slope of the line is 0\boxed{0}.

This result tells us that the line is horizontal.

Would you like more details or have any questions?

Here are 5 related questions:

  1. What is the equation of a horizontal line?
  2. How does the slope of a vertical line differ from a horizontal line?
  3. What does a zero slope indicate about the relationship between the two points?
  4. How can you determine the slope of a line graphically?
  5. What happens to the slope if the points are on a vertical line?

Tip: A slope of 0 always indicates a horizontal line, where all points on the line have the same yy-coordinate.

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Geometry

Formulas

Slope formula

Theorems

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Suitable Grade Level

Grades 6-8