Chapter 1
Linear Equations and Graphing
Course: Gre
Subject: Gre Quantitative Reasoning
Chapter: Inequalities And Absolute Values
What Is a Linear Equation?
A linear equation is an equation whose graph is a straight line. It can be written in several forms, each with its own advantages.
Standard Form
The standard form of a linear equation is:
Ax + By = C
where A, B, and C are real numbers, and A and B are not both zero.
Examples:
- y = 2 (horizontal line) → A = 0, B = 1, C = 2
- x = -1 (vertical line) → A = 1, B = 0, C = -1
- 3x + 4y = 12 → A = 3, B = 4, C = 12
Slope-Intercept Form
The slope-intercept form of a linear equation is:
y = mx + b
where:
- m is the slope (rate of change)
- b is the y-intercept (where the line crosses the y-axis)