Virginia SOL 7.PFA.1.c
The Standard
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 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 graph a proportional relationship from one ordered pair and a given slope. They use rise over run for positive or negative slopes and extend the line through the origin.
What Mastery Looks Like
- Students plot the given point accurately and use the slope as rise over run. They place several points in both directions and draw a straight line through them. Their line passes through the origin.
Common Misconceptions
- Students may treat the given point as the y-intercept. They may reverse rise and run or make both parts negative for a negative slope. Some forget that a proportional graph passes through the origin.
How to Assess It
- On a blank coordinate grid, graph the proportional relationship through (2, -6) with slope -3. Label two more points and explain why (0, 0) lies on the line.
Lesson moves
Ways to Teach It
On a taped coordinate plane, place a marker at the given point, then use rise and run to place three more markers.
Write how the graph changes when the slope switches from 2/3 to -2/3, while the starting point stays at the origin.
Play Slope-Step Relay: teams draw a matched point-and-slope card, plot four points, then check another team's line.
Graph a hiker's elevation change when descending 40 feet per minute, using the point (3, -120) and a slope of -40.
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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.b
Identify and describe a line with a slope that is positive, negative, or zero (0), given a graph.
- 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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