---
title: "8.PAR.4: Linear Relationships and Graphs (Georgia Mathematics standard)"
code: 8.PAR.4
cite_as: Georgia Standards of Excellence, Mathematics, 8.PAR.4
subject: math
grades:
  - grade-8
language: en
canonical_url: https://georgiahomeroom.org/standards/code/8.PAR.4
md_url: https://georgiahomeroom.org/standards/code/8.PAR.4.md
alternate_language_url: https://georgiahomeroom.org/es/standards/code/8.PAR.4.md
source_url: https://case.georgiastandards.org/ims/case/v1p1/CFDocuments/e9dd7229-3558-4df2-85c6-57b8938f6180
source_last_changed: 2024-10-09
data_built: 2026-09-18
publisher: Georgia Homeroom, a free public-interest project of Georgia Civic Data. Not affiliated with or endorsed by the Georgia Department of Education or any school district.
up: https://georgiahomeroom.org/standards/math/grade-8.md
index: https://georgiahomeroom.org/standards/index.md
---

# 8.PAR.4: Linear Relationships and Graphs

Show and explain the connections between proportional and non-proportional relationships, lines, and linear equations; create and interpret graphical mathematical models and use the graphical, mathematical model to explain real phenomena represented in the graph.

- Subject: Mathematics
- Appears in: Grade 8, https://georgiahomeroom.org/standards/math/grade-8.md

## Expectations

- **8.PAR.4.1**: Use the equation y = mx (proportional) for a line through the origin to derive the equation y = mx + b (non-proportional) for a line intersecting the vertical axis at b.
- **8.PAR.4.2**: Show and explain that the graph of an equation representing an applicable situation in two variables is the set of all its solutions plotted in the coordinate plane.

## Georgia Milestones coverage

- Mathematics Grade 8 (EOG). Patterning & Algebraic Reasoning. Show and explain the connections between proportional and non-proportional relationships, lines, and linear equations; create and interpret graphical mathematical models and use the graphical, mathematical model to explain real phenomena represented in the graph. (about 10% of the test; 6 points)

## What mastery looks like

Georgia's Achievement Level Descriptors. The levels are cumulative: each includes the ones before it. Proficient is on grade level.

- **Beginning**: Given an equation in the form y = mx + b and/or the graph of that equation, identify the slope and the y-intercept. Identify points that make a linear equation given in two variables true.
- **Developing**: Explain how the slope and y-intercept change in a graphical representation as the values of m and b change in the equation y = mx + b. Given an equation in slope-intercept form, match/create a graph of the equation.
- **Proficient**: Create the equation y = mx + b when given a graphical representation. Relate graphical mathematical models to applicable situations.
- **Distinguished**: Create and interpret linear graphical mathematical models to explain real phenomena represented in graphs.

## The same standard across grades

- Grade 2, 2.PAR.4: Identify, describe, extend, and create repeating patterns, growing patterns, and shrinking patterns. https://georgiahomeroom.org/standards/code/2.PAR.4.md
- Grade 7, 7.PAR.4: Recognize proportional relationships in relevant, mathematical problems; represent, solve, and explain these relationships with tables, graphs, and equations. https://georgiahomeroom.org/standards/code/7.PAR.4.md
- **Grade 8, 8.PAR.4 (this standard)**: Show and explain the connections between proportional and non-proportional relationships, lines, and linear equations; create and interpret graphical mathematical models and use the graphical, mathematical model to explain real phenomena represented in the graph.

Source: Georgia Standards of Excellence, published by the Georgia Department of Education at case.georgiastandards.org.