Georgia 8.FGR.5.5
The Standard
Write and explain the equations y = mx + b (slope-intercept form), Ax + By = C (standard form), and (y - y₁) = m(x - x₁) (point-slope form) as defining a linear function whose graph is a straight line to reveal and explain different properties of the function.
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 write one linear relationship in slope-intercept, standard, and point-slope forms. They explain which features each form shows most clearly, including slope, intercepts, and known points.
What Mastery Looks Like
- Students can choose a useful equation form from a graph, slope, intercept, or point. They can convert between forms, graph the line, and explain why the equations represent the same function.
Common Misconceptions
- Students may treat equivalent equations as different lines because the forms look different. They often lose a negative sign when solving for y or reverse signs in point-slope form. Some confuse the y-intercept with the x-intercept.
How to Assess It
- Exit ticket: A line passes through (3, 5) with slope -2. Write it in all three forms, then state what each form reveals.
Lesson moves
Ways to Teach It
Give pairs equation, graph, slope, intercept, and point cards to match, then have them justify each set using visible features.
Prompt: Which equation form would you choose to graph quickly, find intercepts, or use a known point, and why?
Play a conversion relay where teams rewrite one line in all three forms and check equivalence by testing two ordered pairs.
Compare taxi plans using fare equations, then rewrite each equation to show starting fee, rate, and a point from a receipt.
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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.4.1
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 a...
- 8.FGR.5.9
Graph and analyze linear functions expressed in various algebraic forms and show key characteristics of the graph to describe applicable situations.
- 8.FGR.6.2
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercepts.
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