Georgia 8.PAR.4.1
The Standard
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.
Georgia's K-12 Mathematics Standards · 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.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students recognize that adding a constant shifts every output of a proportional relationship by the same amount. They identify the rate of change and starting value, then write a linear equation from a graph, table, or context.
What Mastery Looks Like
- Given a graph, table, or situation, a student correctly finds the rate of change and starting value. The student writes the linear equation and explains how the starting value shifts the proportional line.
Common Misconceptions
- Students may assume every linear relationship is proportional and must pass through the origin. They may confuse the starting value with the slope or use the horizontal-axis intercept instead.
How to Assess It
- Exit ticket: A line passes through (0, -3) and (4, 5). Write its equation and explain how it relates to a proportional line with the same slope.
Lesson moves
Ways to Teach It
Give pairs transparent coordinate grids, graph y = 2x, slide the overlay up 3 units, and record how the equation and intercept change.
Ask students to write: How are y = 3x and y = 3x - 4 alike, and what does -4 change in the graph and table?
Run a card sort matching equations, graphs, and tables, including pairs with equal slopes but different vertical-axis intercepts.
Model a taxi fare with a $4 starting fee and $2 per mile, then compare it with a fare having no starting fee.
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Printable 8.PAR.4.1 Worksheet
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