Curriculum placement
Grade 8. This describes the skill, not a learner estimate.
Linear models of a situation
Construct a linear function and interpret its rate and initial value
Problem types
- Total cost of a loan
- Compare borrowing options
- Saving a goal with regular deposits
- Choose a line's equation from its slope and a point
- Complete a line’s slope and intercept
- Explain a model's starting value
- Find the output at zero
- Extend a linear pattern
- Find the first lower price
- Find the graph’s rule
- Choose the graph of a linear rule
- Show the work: write a line from a point
- Hourly wage and starting cost from a table
Builds on
- Comparing functions
- Slope of a line
- Unit rates with fractions · Earlier idea
A unit rate with fractions is the slope of a linear model, such as miles per hour.
- Word problems with signed numbers · Useful idea
Signed changes per step describe a rate of change, and a starting amount is the initial value of a linear model.
- Finding a unit rate · Earlier idea
A unit rate is the slope of a linear model, the change in output per one unit of input.
- Modeling density · Useful idea
A graph of mass against volume is a line whose slope is the density.
- Profit, cost, and taxes · Useful idea
Saving or paying a fixed amount each week is a linear model with a starting amount and a rate.
- Multi-operation word problems · Useful idea
A story with a starting amount and a repeated change is a linear model: start plus rate times number of steps.
Leads to
Related skills
- Average rate of change · Shared foundations
- Proofs that use coordinates · Shared foundations
- Regions defined by inequalities · Shared foundations
- Systems of linear equations · Shared foundations
- What slides, flips, and turns keep the same · Shared foundations
Open the interactive map to explore lessons and skill connections.