8.PAR.4Linear Relationships and Graphs

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

1. Grade 2 · 2.PAR.4

   Identify, describe, extend, and create repeating patterns, growing patterns, and shrinking patterns.

2. Grade 7 · 7.PAR.4

   Recognize proportional relationships in relevant, mathematical problems; represent, solve, and explain these relationships with tables, graphs, and equations.

3. 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.