Unit 7: Standard Form Introduction

The Definition of Standard Form: Linear equations can be written in the form Ax+By=C, where A, B, and C are integers, and A is typically non-negative.

The Concept of Intercepts: The x-intercept is the point where a line crosses the x-axis (y=0), and the y-intercept is where it crosses the y-axis (x=0).

Structural Differences: Standard Form (Ax+By=C) is structurally distinct from Slope-Intercept Form (y=mx+b) and is uniquely useful for finding intercepts and modeling combined totals.

Real-World Modeling: Standard form equations represent scenarios where two distinct independent quantities combine to equal a fixed constant or budget limit.

Identify Intercepts Algebraically: Calculate the x- and y-intercepts from a standard form equation by substituting zero for the opposite variable.

Graph from Standard Form: Plot a linear equation efficiently by identifying, calculating, and connecting its x- and y-intercepts on a coordinate plane.

Convert Between Forms: Algebraically manipulate equations to convert fluidly from Standard Form to Slope-Intercept Form (y=mx+b) and vice versa.

Model Real-World Scenarios: Write standard form equations from word problems involving two unrelated variables with a constant total, and interpret the contextual meaning of the intercepts.

Formative Assessment

Performance Task

Summative Assessment