Big Idea:

Big Idea 1

Linear functions are characterized by a constant rate of change.

1 week

Evidence of Understanding

  • evaluate quantities in a linear equation or inequality with a situation, table of values, or graph
    • recognize the lead coefficient, degree, and constant in any polynomial function 
      • describe linear functions as a subset of polynomial functions with a degree of 1
    • explain the difference between variables and fixed quantities in a function rule
      • given f(x) = mx + b, compare how the constant (b) and the lead coefficient (m) relate to the graph, table, or situation
      • Example: explain how y = 2x + 5 and y = 5x + 2 are different
    • describe how quantities from a situation, table, or graph map to parts of a linear inequality
    • construct a linear equation, inequality, table, graph, situation, or verbal description given any representation of the function
    • describe how the constant and rate of change in a function rule impact domain and range values


  • write a linear equation or inequality in 1 variable from a situation and use it to solve problems
    • determine if a given number is a solution to an equation or inequality
    • understand differences between linear expressionsequations, and inequalities
      • recognize equations map an input with a single output that make the equation true and inequalities map several possible outputs for a single input that make the inequality true
    • in the form px + q = r where p, q, and r are rational numbers, describe how r is one specific output value of the general function f(x) = px + q 
      • identify units for each term and explain what each term represents in the function
    • articulate (p, r), (x, r), (q, r) as possible function relationships and understand why (p, q), (x, q), and (p, x) do not make sense as a function relationship (spiral back to Unit 1, Big Idea 1)
    • in the form px + q = r, describe how increasing or decreasing p, q, or r impacts x
    • represent an equation or inequality in 1 variable using a visual diagram or model


Develop conceptual understanding:

expression, equation, inequality, variable, fixed quantity, coefficient, constant, rational, equality, equal, reasonable

Supporting terms to communicate:

function, function rule, initial value, rate of change, domain, range, dependent, independent, linear equation, greater than, greater than or equal to, less than, less than or equal to, at least, at most

Core Resource
A core resource supports multiple days of instruction.
  • Generating Equations and Inequalities
    This multiple-day resource supports students in generating equations and inequalities from situations.
    Generating Equations and Inequalities

    During these three activities, students focus on the relationships between quantities described in situations and represent those relationships using tables of values, graphs, and function rules. Students then explore what happens to those representations when the parameters embedded within the situations change.