Math Problem Statement

Parallel to y=-6 through the point (-2,-5)

Solution

To find the equation of a line parallel to y=6y = -6 that passes through the point (2,5)(-2, -5), we can analyze the form of the given line and apply parallel line properties.

  1. The line y=6y = -6 is a horizontal line, where every point on the line has yy-coordinate 6-6. This means the slope of the line is zero (since it does not change in the yy-direction).

  2. A line parallel to y=6y = -6 will also be horizontal, maintaining a slope of zero.

  3. Since the line must pass through the point (2,5)(-2, -5), its yy-coordinate must be 5-5.

Thus, the equation of the line parallel to y=6y = -6 through the point (2,5)(-2, -5) is: y=5y = -5

This line is horizontal, passing through all points where y=5y = -5.

Would you like more details on horizontal and vertical lines, or do you have any questions?

Here are some related questions for further exploration:

  1. How do you find the equation of a line perpendicular to y=6y = -6?
  2. What is the equation of a line parallel to x=3x = -3 through a given point?
  3. How do you find the slope of a line given two points on the line?
  4. What is the distance between the lines y=6y = -6 and y=5y = -5?
  5. How can we find the intersection of a horizontal and a vertical line?

Tip: For any horizontal line, the equation will always be y=constanty = \text{constant}, where the constant is the yy-coordinate of any point on the line.

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Math Problem Analysis

Mathematical Concepts

Analytic Geometry
Equations of Parallel and Horizontal Lines

Formulas

Equation of a horizontal line: y = constant

Theorems

Properties of Parallel Lines

Suitable Grade Level

Grades 8-10