Section 13.4 Closing Ideas
The slope-intercept form of a line has many useful applications and interpretations. For example:
The can be interpreted as a one-time initiation fee and the slope can be interpreted as a per-use expense. So the cost of an exercise program with a $15 initiation fee and $4 per-use fee can be modeled by \(y = 4x + 15\text{,}\) where \(y\) is the total cost and \(x\) is the number of uses.
The can be interpreted as an initial investment expense (as negative value), and the slope can be interpreted as a per-unit profit for a business model. So if raw materials cost $100 but each item that can be created sells for $12 each, then the profit \(y\) can be modeled as \(y = 12x - 100\text{,}\) where \(x\) represents the number of items sold.
The slope-intercept form of a line is the standard way that computers present a line of best fit.
There is a lot more than can be said about the use of lines in applications, but those will have to wait for their corresponding courses. At this point, the goal is that you are comfortable enough with the algebra of two-variable equations to convert them into slope-intercept form, and that you are able to sketch the graphs of such lines.