Virginia SOL 8.PFA.3.a
The Standard
Determine how adding a constant (b) to the equation of a proportional relationship y = mx will translate the line on a graph.
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 compare a proportional line with a related line that has a constant added. They describe the vertical shift, locate the new y-intercept, and recognize that the slope does not change.
What Mastery Looks Like
- Students predict that a positive constant moves every point up and a negative constant moves every point down. They identify the new y-intercept as (0, b) and explain that the slope stays the same.
Common Misconceptions
- Students may treat b as a horizontal shift or believe it changes the line’s steepness. They may move negative values upward or name the y-intercept as (b, 0).
How to Assess It
- Exit ticket: Compare y = -2x and y = -2x + 4. State the shift, slope, and new y-intercept.
Lesson moves
Ways to Teach It
On transparent coordinate grids, graph y = 2x, overlay y = 2x + 3 and y = 2x - 2, then describe each shift.
Ask, “How can you predict the new line from the sign and size of b without plotting points?” Students justify with examples.
Run a card sort matching equations, graphs, y-intercepts, and shift descriptions for lines with the same slope.
Compare taxi costs with the same per-mile rate but different starting fees, then graph how each fee moves the cost line.
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Printable 8.PFA.3.a Worksheet
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Related Standards
- 7.PFA.1.d
Graph a line representing a proportional relationship between two quantities given the equation of the line in the form y = mx, where m represents the slope as ...
- 7.PFA.1.c
Graph a line representing a proportional relationship, between two quantities given an ordered pair on the line and the slope, m, as rate of change. Slope may i...
- 7.PFA.1.a
Determine the slope, m, as the rate of change in a proportional relationship between two quantities given a table of values, graph, or contextual situation and ...
- 8.PFA.3.e
Write an equation of a linear function in the form y = mx + b, given a graph, table, or a situation in context.
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