Lesson Plan

Two-Variable Equations and Inequalities


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Big Ideas




Students will understand the connection between equations and slope-intercept form and solve/graph two-variable equations and inequalities. They will:

  • represent real-world scenarios with two-variable equations and inequalities.
  • find solutions to two-variable equations and inequalities.
  • write an equation in slope-intercept form.
  • solve a two-variable equation for one variable.
  • solve a two-variable inequality for one variable.
  • graph two-variable linear equations and inequalities.

Essential Questions

  • How can mathematics support effective communication?
  • How are relationships represented mathematically?
  • How can expressions, equations and inequalities, be used to quantify, solve, model, and/or analyze mathematical situations?
  • How can data be organized and represented to provide insight into the relationship between quantities?


  • Coefficient: The coefficient of a term in an expression is the number that is multiplied by one or more variables or powers of variables in the term.
  • Function: A relation in which every input value has a unique output value.
  • Linear Equation: An equation of the form Ax + By = C, where A ≠ 0 and B ≠ 0. The graph of a linear equation is a straight line.
  • Rate of Change: The ratio of the change in the output value and change in the input value of a function.
  • Simultaneous Linear Equations: Two or more linear equations that share a set of variables and either exactly one solution, no solutions, or infinitely many solutions; often called a “system of equations.”
  • Slope: The measure of the steepness of a line; the ratio of the change in the y-values to the x-values of the linear function; rate of change.
  • y-intercept: The y-coordinate of the point where a line intersects the y-axis; the value of the function when x = 0.


90–120 minutes

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