Curriculum placement
Grade 8. This describes the skill, not a learner estimate.
Slope of a line
Find and interpret slope from points tables and graphs
Problem types
- Slope through two points
- Decide the sign of a slope from how the variables change
- Slope and intercept from points and equations
- Graph a line from its equation
- Compare two slope triangles
- Slope from a graph
- Look past the step sizes
- Why slope triangles give the same slope
- Order the slope triangle argument
- Derive the equation of a line from its slope
Builds on
- Representing a proportional relationship
- Coordinates in four quadrants
- Dilations and similarity · Useful idea
Scaling a right triangle's horizontal and vertical changes by the same factor preserves their ratio. This explains why triangles along one straight line give the same slope.
- Unit rates with fractions · Useful idea
Slope is a unit rate: the change in vertical distance per one unit of horizontal change.
- Equivalent ratios · Earlier idea
Equal steps in a ratio table give a constant ratio of change, which is the slope of the line through its points.
Leads to
- Comparing functions
- Linear models of a situation
- Systems of linear equations
- What slides, flips, and turns keep the same
- Average rate of change
- Regions defined by inequalities
- Proofs that use coordinates
- Graphs of quadratic functions · Extend the idea
A line is graphed from two points because its slope is constant. A parabola has no constant slope, so it is graphed from its vertex and symmetric points found by substituting.
Related skills
- Distance in the coordinate plane · Shared foundations
- Side lengths from coordinates · Shared foundations
- A graph as the solution set · Shared foundations
- Translations, reflections, and rotations · Shared foundations
- Scale drawings of lengths and areas · Shared foundations
Open the interactive map to explore lessons and skill connections.