Curriculum placement
Algebra 1. This describes the skill, not a learner estimate.
Linear equations from constraints
Construct linear equations from constraints and explain solutions
Problem types
- Meaning of slope and initial value
- Write a line in a requested form
- Parallel, perpendicular and axis-parallel lines
- Combine rates in a word problem
- Enter a combined-rate or mixture value
- Choose a two-variable equation for a total
- Build and solve a linear model
- Choose the linear model
- Fee plans: recover a rate, compare plans or find elapsed time
- Choose the rule for a flat fee that covers the first hours
- Choose the point-slope equation of the line through two points
- Equation of a line from a table with uneven steps
Builds on
- Linear equations with variables on both sides
- Linear models of a situation
- Naming the quantities in a model · Useful idea
A linear equation for a situation needs defined quantities first: a variable with units for each changing quantity, and a rate in dependent unit per independent unit.
- Slopes of parallel and perpendicular lines · Useful idea
Parallel and perpendicular lines have equations with equal or negative reciprocal slopes, used to write the equation of a line.
- Rational equations with one denominator · Useful idea
Two workers' rates combine as reciprocals of times, so finding a shared time solves a rational equation.
- Dependent and independent variables · Earlier idea
Naming the independent and dependent variable sets up a linear equation whose slope and intercept have meaning in the situation.
- Multi-step word problems · Useful idea
A multistep story with an unknown total is written as a linear equation whose coefficients are rates and whose constant is a starting amount.
Leads to
- Systems that model two constraints · Extend the idea
One linear model extends to two models compared together, where the solution is when they agree.
- Reading slope and intercept in context · See it applied
A fitted line is a linear model, with slope as a rate and intercept as a starting value.
- Solving inequalities · See it applied
A charge made of a fee plus a rate is a linear model. Asking which counts keep the charge within a budget turns the equation into an inequality that is solved the same way.
- Motion described by a parameter · See it applied
Position at constant velocity is a linear model in time, which parametric equations write for each coordinate.
Related skills
- Rules for an arithmetic sequence · Shared foundations
- Why each equation step is valid · Shared foundations
- Rearranging a formula · Shared foundations
- A graph as the solution set · Shared foundations
- Systems of linear equations · Shared foundations
Open the interactive map to explore lessons and skill connections.