Virginia SOL 7.PFA.1.d
The Standard
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 rate of change. Slope may include positive or negative values.
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 use the coefficient of x to determine how a line rises or falls across a coordinate plane. They plot points that follow the rate and draw a straight line through the origin.
What Mastery Looks Like
- Students identify the coefficient of x as the slope and describe it as a rate of change. They graph a straight line through the origin, with the correct steepness and direction, and verify points in the equation.
Common Misconceptions
- Students may plot the slope as a y-intercept instead of starting at the origin. They may reverse rise and run, ignore a negative sign, or plot points that do not form a straight line.
How to Assess It
- Give students y = -1.5x and a blank coordinate grid. Ask them to graph the line, label two points, and explain how the slope determined each point.
Lesson moves
Ways to Teach It
Use a taped floor grid and have students step from the origin using the rise and run for positive and negative slopes.
Ask students to compare y = 2x and y = -2x, then write how the sign changes the graph.
Play Slope Match with cards showing equations, graphs, tables, and rates, and have teams build matching sets.
Graph the change in a tank's water volume over time when water drains at 3 gallons per minute.
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Printable 7.PFA.1.d Worksheet
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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.
- 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 ...
- 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...
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