Maryland Math 8.AT.A.2
Standard Cluster
Use proportional reasoning to identify slope and represent linear relationships. Use proportional reasoning to explain why the slope m is the same between any two points on a non-vertical line by showing that the ratios of vertical change to horizontal change between points are equivalent. Use this relationship to write equations of lines in the form y = mx for lines that pass through the origin, and in the form y = mx + b for lines that include a vertical shift from the origin, where b represents the y-intercept.
Maryland College and Career Ready Standards for Mathematics (2025) · USE PROPORTIONAL RELATIONSHIPS TO REPRESENT AND REASON ABOUT LINEAR EQUATIONS.
Cluster contents
Standards in This Cluster
8.AT.A.2 is a cluster heading. These are the individual standards under it.
- 8.AT.A.2.a
Use proportional reasoning to explain why the slope m is the same between any two points on a non-vertical line by showing that the ratios of vertical change to...
- 8.AT.A.2.b
Use this relationship to write equations of lines in the form y = mx for lines that pass through the origin, and in the form y = mx + b for lines that include a...
Teacher's field guide
What This Cluster Means
What Students Need to Do
- Students find slope by dividing vertical change by horizontal change. They use equal rise-to-run ratios to explain why the slope stays the same along a line. They write y = mx for lines through the origin and y = mx + b for lines with a different y-intercept.
What Mastery Looks Like
- Given (0, 2), (2, 5), and (4, 8), a student finds slope ratios of 3/2 and 6/4 and explains why they match. They write y = (3/2)x + 2 and identify 2 as the y-intercept. For a line with the same slope through the origin, they write y = (3/2)x.
Common Misconceptions
- Students sometimes divide y by x to find slope even when the line does not pass through the origin. They may switch rise and run or treat the y-intercept as part of the slope. Some give a vertical line a slope of zero, though its slope is undefined.
How to Assess It
- Exit ticket: For (0, 2), (2, 5), and (4, 8), find the slope using two different pairs and explain why the ratios match. Write equations for this line and a line with the same slope through (0, 0).
Lesson moves
Ways to Teach It
On graph paper, plot (0, 2), (2, 5), and (4, 8); draw two slope triangles and compare their rise-to-run ratios.
Ask students why 6/4 and 3/2 describe the same slope on a line through (0, 2).
Match graph cards to slope cards and equation cards for y = 2x and y = 2x + 3.
Make a taxi fare table with a $4 pickup charge and $2 per mile; compare fare changes and write y = 2x + 4.
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Printable 8.AT.A.2 Worksheet
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Related Standards
- 8.AT.A.1.a
Graph proportional relationships and interpret the unit rate as the slope of the graph.
- 8.AT.A.1.b
Compare proportional relationships represented in different forms (e.g., graphs, equations, and tables) by analyzing their slopes.
- 8.AT.A.1
Analyze and compare proportional relationships using slope.
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