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This Linear models word problems exercise appears under the 8th grade (U.S.) Math Mission, Algebra I Math Mission, Mathematics II Math Mission, Algebra II Math Mission and Mathematics III Math Mission. This exercise has a mix of various constructing and interpreting of linear models with various different possible forms of the functions.

Types of Problems

There are seven types of problems in this exercise:

  1. Construct the graph that comes with the change: This problem describes a word problem that is modeled in a graph. The user is told a change that will happen, and they are asked to redraw the graph subject to this change.
    Cailf1

    Construct the graph that comes with the change

  2. Select the statements that describe the graph: This problem provides a graph and several statements that may or may not be true. The user is asked to select if one or the other or both or neither of the statements are in fact true.
    Cailf2

    Select the statements that describe the graph

  3. Select the statements that describe the chart: This problem provides a chart and several statements that may or may not be true. The user is asked to select if one or the other or both or neither of the statements are in fact true.
    Cailf3

    Select the statements that describe the chart

  4. Select the statements that describe the formula: This problem provides a formula and several statements that may or may not be true. Users are asked to select if one or the other or both or neither of the statements are in fact true.
    Cailf7

    Select the statements that describe the formula

  5. Use the chart to find a slope: This problem provides some information and effectively asks users to find the slope of the graph.
    Cailf4

    Use the chart to find a slope

  6. Make the line described: This problem describes some information about a line and asks the user make the graph on the coordinate grid manipulative.
    Cailf5

    Make the line described

  7. Make the linear model described: This problem describes some contextual information about a linear model. The user is expected to create the graph of the model in the space provided.
    Cailf6

    Make the linear model described

Strategies

Knowledge of the various representations of a line (numerical in a chart, algebraic by a formula, and geometric as a graph) are important to doing this exercise well.

  1. The y-intercept is the initial value of the word problem.
  2. The slope is the unit change of a linear function.

Real-life applications

  1. Lines have many applications in business and the sciences.
  2. Intercepts tend to be initial conditions, and slope is the unit rate of change to move along the x-axis units. (In physics, time, in business, units created, etc.)
  3. Slope is almost the derivative, a big idea in the calculus.
  4. The remodel of the SAT is supposed to include more intensive interpretation problems, so this exercise may be a good start eventually.
  5. Knowledge of algebra is essential for higher math levels like trigonometry and calculus. Algebra also has countless applications in the real world.

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