Math Problem Statement

Graph the line by plotting two points. y=−1

Solution

The equation y=1y = -1 represents a horizontal line that crosses the y-axis at y=1y = -1. Since the value of yy is always 1-1, no matter the value of xx, the line is parallel to the x-axis.

Steps to plot the line:

  1. Choose two values for xx. For simplicity, let's pick x=0x = 0 and x=2x = 2.
  2. For both values of xx, the value of yy is always 1-1.
    • When x=0x = 0, y=1y = -1, so the point is (0,1)(0, -1).
    • When x=2x = 2, y=1y = -1, so the point is (2,1)(2, -1).
  3. Plot these two points: (0,1)(0, -1) and (2,1)(2, -1).
  4. Draw a straight line through these two points.

The line will be horizontal, at a constant value of y=1y = -1.

Would you like me to explain any steps further, or would you like to explore something else? Here are 5 related questions:

  1. What is the general form of the equation of a horizontal line?
  2. How can you find the slope of a horizontal line?
  3. What happens to the graph of y=1y = -1 when you add a number to it, like y=1+3y = -1 + 3?
  4. How does a vertical line differ from a horizontal line in terms of equations and graphs?
  5. How can you graph the equation y=2x+3y = 2x + 3?

Tip: For horizontal lines, the equation will always be in the form y=cy = c, where cc is a constant.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Coordinate Geometry

Formulas

y = c (for horizontal lines)

Theorems

Properties of horizontal lines

Suitable Grade Level

Grades 7-9