Virginia SOL 8.PFA.3.e
The Standard
Write an equation of a linear function in the form y = mx + b, given a graph, table, or a situation in context.
Virginia Standards of Learning for Mathematics · The student will represent and solve problems, including those in context, by using linear functions and analyzing their key characteristics (the value of the y-intercept (b) and the coordinates of the ordered pairs in graphs will be limited to integers).
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students identify the rate of change and starting value in a graph, table, or situation. They use those values as m and b to write an equation in the form y = mx + b.
What Mastery Looks Like
- Students find the slope and y-intercept from a graph, table, or situation. They write the correct equation and verify it with a point or value from the representation.
Common Misconceptions
- Students may use the x-intercept as b or treat any y-value as the y-intercept. They may reverse rise and run, miss skipped x-values, or swap m and b.
How to Assess It
- Exit ticket: The table contains points (0, 3), (2, 7), and (4, 11). Write y = mx + b, then label m and b.
Lesson moves
Ways to Teach It
Tape a coordinate grid on the floor, place students at plotted points, and use rise and run to build the equation.
Ask students to explain how a table reveals m and b, especially when x increases by more than one.
Give groups cards showing graphs, tables, situations, and equations, then have them match each set and justify their choices.
Present a taxi fare with a $4 starting fee and $2 per mile, then have students write and interpret the equation.
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Related Standards
- 8.PFA.3.a
Determine how adding a constant (b) to the equation of a proportional relationship y = mx will translate the line on a graph.
- 8.PFA.3.c
Graph a linear function given a table, equation, or a situation in context.
- 8.PFA.3.d
Create a table of values for a linear function given a graph, equation in the form of y = mx + b, or context.
- 8.PFA.3.f
Create a context for a linear function given a graph, table, or equation in the form y = mx + b.
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