Georgia 8.FGR.5.9
The Standard
Graph and analyze linear functions expressed in various algebraic forms and show key characteristics of the graph to describe applicable situations.
Georgia's K-12 Mathematics Standards · Describe the properties of functions to define, evaluate, and compare relationships, and use functions and graphs of functions to model and explain real phenomena.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students graph linear functions written in different equation forms. They identify slope, intercepts, and increasing or decreasing behavior, then connect those features to a situation.
What Mastery Looks Like
- Students accurately graph an equation written in slope-intercept, standard, or point-slope form. They identify and interpret slope, intercepts, and whether the function increases or decreases in a given situation.
Common Misconceptions
- Students may switch the rise and run, miss a negative slope, or treat the y-intercept as an ordered pair without using zero for x. They may think equations in different forms represent different functions. Some students connect points instead of using the constant rate of change.
How to Assess It
- Give students 2y + 4x = 8. Ask them to graph it, label the slope and intercepts, and write one sentence describing its behavior.
Lesson moves
Ways to Teach It
Place tape axes on the floor, give students equation cards, and have them stand at points that form each line.
Ask students to explain why 2x + y = 6 and y = -2x + 6 produce the same graph.
Use a card sort matching equations, graphs, slopes, intercepts, and situation descriptions, then have pairs justify each match.
Graph a taxi fare with a starting fee and per-mile charge, then label what the slope and y-intercept mean.
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Printable 8.FGR.5.9 Worksheet
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Related Standards
- 8.FGR.5.6
Write a linear function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
- 8.PAR.4
Show and explain the connections between proportional and non-proportional relationships, lines, and linear equations; create and interpret graphical mathematic...
- 8.FGR.5.2
Within realistic situations, identify and describe examples of functions that are linear or nonlinear. Sketch a graph that exhibits the qualitative features of ...
- 8.FGR.5.3
Relate the domain of a linear function to its graph and where applicable to the quantitative relationship it describes.
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