Then $1.29c$ gives us the total amount we pay for chicken, and $3.49s$ gives us the total amount we pay for steak. So, let us assign variables to those two quantities. We don't know how many pounds of chicken and steak we are buying. Therefore, all solutions are approximate.Ĭhicken costs \$1.29 per pound and steak costs \$3.49. Note that all numbers are rounded to two digits after the decimal. It is especially useful for students to see that, for example, the "steak-intercept" is interpreted in the same way regardless of whether the vertical or horizontal axis is the "steak-axis." This task presents a good opportunity to have a discussion about choosing independent and dependent variables and interpreting slopes, intercepts, and generic points on the graph in the context. To fully explore part (b), students should interpret the horizontal and vertical intercepts of the graph, the slope of the graph, and the coordinates of points on the graph. Whenever we have a (non-constant) linear relationship between two quantities, we can always write either quantity as a function of the other, and students should understand that which variable is the dependent variable and which is the independent variable is a choice made by the modeler.
Part (a) is relatively straightforward, although the wording is left intentionally ambiguous about whether the amount of steak should be written as a function of the amount of chicken or the amount of chicken as a function of the amount of steak (both approaches are presented in the solutions shown below). This task presents a real world situation that can be modeled with a linear function best suited for an instructional context.
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