Maryland Math 8.AT.A.2.b
The Standard
- 8.AT.A.2
- Use proportional reasoning to identify slope and represent linear relationships.
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.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the slope and y-intercept from a graph, table, or situation. They write y = mx for lines through the origin and y = mx + b for lines that start elsewhere.
What Mastery Looks Like
- Given points (0, -1) and (3, 5), a student writes y = 2x - 1 and checks both points. They explain that 2 is the change per x-unit and -1 is the value when x = 0.
Common Misconceptions
- Students may use the x-intercept for b or divide the run by the rise to find the slope. Some assume every line starts at zero or mistake b for the change per x-unit.
How to Assess It
- Exit ticket: A line passes through (0, 3) and (2, 7). Write its equation and label its slope and y-intercept.
Lesson moves
Ways to Teach It
Place counters at (0, 2), (1, 5), and (2, 8) on graph paper; draw the line and write its equation.
Ask partners to plot y = 3x and y = 3x + 2, then explain why the lines start at different heights.
Match cards for y = 2x, y = 2x + 3, y = -x, and y = -x + 3 to four hand-drawn graphs.
A taxi charges $4 to start and $2 per mile; write its cost equation and compare it with a taxi that has no starting fee.
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Related Standards
- 8.AT.D.9
Interpret the graph of a linear function in the form y = mx + b
- 8.AT.D.9.a
Given the graph of a linear function, identify the slope and y-intercept.
- 8.DS.B.4
Use a provided linear model to make predictions based on bivariate measurement data. Interpret the meaning of the slope and y-intercept in context.
- 8.AT.D.9.b
Match a linear equation in the form y = mx + b to its graph.
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