Math Problem Statement

Graph the following equation in a rectangular coordinate system. x=-4

Solution

The equation x=4x = -4 represents a vertical line in the rectangular coordinate system. Since the equation gives a constant value for xx, the line is vertical and passes through x=4x = -4 for all values of yy.

I can describe or graph it for you:

  • The line is parallel to the yy-axis.
  • The line crosses the xx-axis at (4,0)(-4, 0), but continues infinitely both upwards and downwards, for all yy-values.

Would you like me to create a visual representation of this graph?

Here are 5 related questions:

  1. What does a horizontal line equation look like?
  2. How do you determine the slope of a vertical line?
  3. How does the graph of y=4y = -4 differ from x=4x = -4?
  4. What happens when you graph a line parallel to the xx-axis?
  5. How do you write the equation of a line parallel to x=4x = -4 but shifted 3 units to the right?

Tip: A vertical line has an undefined slope, as there is no change in yy for any change in xx.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Coordinate Geometry

Formulas

Equation of a vertical line: x = constant

Theorems

Vertical Line Theorem: A line with the equation x = constant is vertical and parallel to the y-axis.

Suitable Grade Level

Grades 6-8