🔟elementary algebra review

key term - Y = b

Definition

The equation 'y = b' represents a horizontal line on a coordinate plane, where 'b' is the constant value that the y-coordinate takes on. This equation is a special case of a linear equation in two variables, where the slope of the line is zero, and the y-value remains constant regardless of the x-value.

5 Must Know Facts For Your Next Test

  1. The equation 'y = b' represents a horizontal line that is parallel to the x-axis, with a constant y-value of 'b'.
  2. When the slope of a linear equation is zero, the line is horizontal, and the equation can be simplified to 'y = b'.
  3. The graph of the equation 'y = b' is a straight, horizontal line that intersects the y-axis at the point (0, b).
  4. The equation 'y = b' can be used to represent constant values, such as the height of a building or the altitude of an aircraft.
  5. Solving the equation 'y = b' for 'y' results in 'y = b', indicating that the y-coordinate is always equal to the constant 'b'.

Review Questions

  • Explain how the equation 'y = b' differs from a general linear equation in two variables.
    • The equation 'y = b' is a special case of a linear equation in two variables, where the slope of the line is zero. This means that the y-coordinate remains constant, regardless of the value of the x-coordinate. In contrast, a general linear equation in two variables, 'y = mx + b', has a non-zero slope 'm' that determines the rate of change between the x and y variables.
  • Describe the graphical representation of the equation 'y = b' on a coordinate plane.
    • The graph of the equation 'y = b' is a horizontal line that is parallel to the x-axis. Since the y-coordinate is constant, the line will intersect the y-axis at the point (0, b). The line will have a slope of zero, meaning that it does not change in the vertical direction as the x-value changes. This type of line is often used to represent constant values, such as the height of a building or the altitude of an aircraft.
  • Analyze the relationship between the equation 'y = b' and the concept of a constant function.
    • The equation 'y = b' can be considered a constant function, where the output (y-value) is always equal to the constant 'b', regardless of the input (x-value). This means that the function has a constant rate of change, or a slope of zero, and the y-value does not depend on the x-value. Constant functions are often used to model situations where a quantity remains fixed or unchanging, such as the cost of a product or the interest rate on a loan.