Linear Relationships: Slope, Proportionality, and Systems: Math Unit 6, Grade 8 (Letters & Devotion)

Description

Linear Relationships: Slope, Proportionality, and Systems is Unit 6 of Pre-Algebra: Foundations for Algebra I (Grade 8), the Letters & Devotion Math course, complete in one printable PDF: 13 lessons, the unit check-up and the answer key, 75 pages.

• Similar-triangle justification for constant slope on a non-vertical line
• The slope formula (y2-y1)/(x2-x1) applied to two coordinate points
• Proportional relationships graphed as lines through the origin, with slope equal to unit rate
• Unit rate comparison across mixed representations of proportional relationships
• Slope-intercept form as a graphing and interpreting tool
• The origin test distinguishing proportional from non-proportional linear relationships
• The intersection point of two graphed lines as the system’s solution
• The meaning of an intersection point as a shared input-output pair in a modeled context
• The substitution method for solving a 2×2 linear system
• Strategic variable selection prior to substitution
• The one/none/infinite solution cases for a linear system, linked to identity and contradiction equations
• System-of-equations modeling of a scenario from an unpracticed domain
• Structural reasoning about simultaneous intersection using slope and intercept comparisons rather than computation

Every lesson is written for a parent with no teaching background: it opens with a short script to read aloud, names the specific wrong idea a student is likely to reach for and how to correct it, and closes with a practice sheet you may copy for your household. Scripture references are King James Version throughout. Black-and-white, 8.5 x 11 in. The whole year of this course is also in this store as a single book.

AI note: The written content of this resource was drafted with AI tools, then reviewed and edited by the author.