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Mathematics · Grade 8

Proportional Relationships and Slope

Learners connect the unit rate of a proportional relationship to the slope of its graph and compare proportional relationships given as equations, tables, graphs and descriptions. They use slope triangles and similar triangles to explain why a line has one constant slope, compute slopes from two points, and derive and graph y = mx and y = mx + b.

  • 4 lessons
  • About 95 minutes
  • Proportional relationships and slope check: 10 questions
  • Ways to answer: choose an answer, type a fraction, draw a graph, plot points, match pairs and type a number
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What learners will discover

  • Graph proportional relationships and interpret the unit rate as the slope of the graph.
  • Compare two proportional relationships represented in different ways (equation, table, graph or description).
  • Find the slope of a line from two points or a slope triangle, and use similar triangles to explain why the slope is the same between any two points on a non-vertical line.
  • Write and graph equations y = mx for lines through the origin and y = mx + b for lines that cross the y-axis at b.

Lessons

  1. Unit rate is slope 8 steps4 practiceabout 22 min
  2. Comparing proportional relationships 8 steps5 practiceabout 22 min
  3. Slope triangles and similar triangles 9 steps5 practiceabout 25 min
  4. From slope to y = mx + b 9 steps5 practiceabout 26 min
  5. Proportional relationships and slope check 10 questions at the end

Keep exploring

Games to practice with

  • Number-Line HopHelp the frog hop to the right number — from counting to negative fractions.
  • Algebra BalanceKeep the scale level and the equation true, step by step.
  • Function FactoryFeed the machine, crack its rule and predict what comes out.

More 8th grade math

Guide for grown-ups