Virginia SOL 7.PFA.1.a
The Standard
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 write an equation in the form y = mx to represent the direct variation relationship. Slope may include positive or negative values (slope will be limited to positive values in a contextual situation).
Virginia Standards of Learning for Mathematics · The student will investigate and analyze proportional relationships between two quantities using verbal descriptions, tables, equations in y = mx form, and graphs, including problems in context.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the constant rate relating two proportional quantities from a table, graph, or situation. They treat that rate as the slope. They write an equation in the form y = mx.
What Mastery Looks Like
- Students calculate the same y/x ratio across a table or use rise over run on a graph. They identify the correct sign and write y = mx with no added constant. They can explain the slope as a rate with units when context is given.
Common Misconceptions
- Students may divide x by y instead of y by x. They may use differences within one column rather than compare changes in both quantities. Some add a nonzero constant, miss a negative slope, or assume every linear relationship is proportional.
How to Assess It
- Give the table x: 2, 5, 8 and y: 7, 17.5, 28. Ask students to find the slope and write the matching equation.
Lesson moves
Ways to Teach It
Pour water into a marked cylinder for 10-second intervals, record the volume, graph the pairs, and write an equation.
Ask, “How can you tell from a table, graph, or equation that two quantities are proportional?”
Match table, graph, equation, and slope cards, including cards with positive and negative slopes.
Use grocery prices to find cost per item, write a cost equation, and predict the price of another quantity.
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Printable 7.PFA.1.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.e
Make connections between and among representations of a proportional relationship between two quantities using problems in context, tables, equations, and graph...
- 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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