Linear models word problems

The  exercise appears under the 8th Grade Math Mission. This exercise has an eclectic 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 student is told a change that will happen, and they are asked to redraw the graph subject to this change.Cailf1.png
 * 2) Select the statements that describe the graph: This problem provides a graph and several statements that may or may not be true. The student is asked to select if one or the other or both or neither of the statements are in fact true.Cailf2.png
 * 3) Select the statements that describe the chart: This problem provides a chart and several statements that may or may not be true. The student is asked to select if one or the other or both or neither of the statements are in fact true.Cailf3.png
 * 4) Select the statements that describe the formula: This problem provides a formula and several statements that may or may not be true. The student is asked to select if one or the other or both or neither of the statements are in fact true.Cailf7.png
 * 5)  Use the chart to find a slope: This problem provides some information and effectively asks the student to find the slope of the graph.Cailf4.png
 * 6) Make the line described: This problem describes some information about a line and asks the student to make the graph on the coordinate grid manipulative.Cailf5.png
 * 7) Make the linear model described: This problem describes some contextual information about a linear model. The student is expected to create the graph of the model in the space provided.Cailf6.png

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.