Chapter 1
Numbers and Operations
Course: Gace Middle Grades Math 4 8 704
Subject: Gace Middle Grades Math 4 8 704
Chapter: Algebra
1. Determines the equation of a line from information presented in various forms (e.g., table, graph, description)
A linear relationship describes a constant rate of change between two variables. To determine the equation of a line, slope (m) and intercept (b) must be identified. The general form is y = mx + b.
From a table of values:
- Identify two points, such as (x₁, y₁) and (x₂, y₂).
- Calculate slope as m = (y₂ – y₁) / (x₂ – x₁).
- Use one point to solve for the y-intercept b by substituting into y = mx + b.
Example: Table has points (1, 3) and (3, 7). Slope m = (7 – 3) / (3 – 1) = 4/2 = 2. Equation using point (1, 3): 3 = 2(1) + b → b = 1. Equation: y = 2x + 1.