What is the First Degree Equation of a Graph?

The first degree equation of a graph represents a straight line.

A first-degree equation, also known as a linear equation, involving two variables (typically x and y) can be expressed in several forms, all of which depict a straight line when graphed. Let's explore the common forms:

Common Forms of Linear Equations:

• Slope-Intercept Form: This is arguably the most recognizable form:

  • Equation: y = mx + b
  • Where:
    • m represents the slope of the line (the rate of change of y with respect to x).
    • b represents the y-intercept (the point where the line crosses the y-axis).

  Example: y = 2x + 3 has a slope of 2 and a y-intercept of 3.

• Standard Form: Another common form:

  • Equation: Ax + By = C
  • Where:
    • A, B, and C are constants, and A and B are not both zero.
    • This form is useful for finding intercepts.

  Example: 3x + 4y = 12

• Point-Slope Form: Useful when you know a point on the line and the slope:

  • Equation: y - y1 = m(x - x1)
  • Where:
    • m is the slope of the line.
    • (x1, y1) is a known point on the line.

  Example: If a line has a slope of -1 and passes through the point (2, 5), its equation is y - 5 = -1(x - 2).

Key Characteristics of First Degree Equations:

• No exponents greater than 1: The variables x and y are raised to the power of 1 (or implicitly to the power of 1). Equations with terms like x² or y³ are not first-degree equations.

• Straight Line Representation: When graphed on a coordinate plane, a first-degree equation always produces a straight line.

• Constant Rate of Change: The slope of the line is constant throughout, indicating a consistent relationship between x and y.

In summary, the first degree equation of a graph represents a straight line and can be expressed in various forms such as slope-intercept, standard, and point-slope form. These forms are all interconvertible and represent the same linear relationship.