CCSS.Math.Content.8.EE.B.6
The standard
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
Common Core State Standards for Mathematics · Expressions and Equations
What this standard means
Students need to connect the steepness of a line to similar right triangles drawn between pairs of points. They should see that the rise-to-run ratio stays the same anywhere on a non-vertical line, because the triangles have the same shape.
Mastery looks like explaining slope with a diagram, not just using a formula. Students can use a graph to write y = mx for a line through the origin and y = mx + b when the line crosses the y-axis elsewhere. Common stuck points are mixing up rise and run, treating b as slope, and not seeing why vertical lines are different.
Ways to teach it
- Have students draw three slope triangles on the same line using graph paper, then compare each rise, run, and rise divided by run.
- Ask students to explain in writing why two different point pairs on the same line give the same slope.
- Give an exit ticket with one graphed line and ask for slope, y-intercept, and the equation.
- Use a wheelchair ramp diagram and ask students how similar triangles show the ramp has one constant steepness.
Plan a lesson for CCSS.Math.Content.8.EE.B.6
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Related standards
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Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicu...
- CCSS.Math.Content.8.SP.A.3
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.
- CCSS.Math.Content.HSS-ID.C.7
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
- CCSS.Math.Content.8.F.A.3
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.