graph. Not all values for could be represented and connecting the points would not be x appropriate. Example: The function = + 20 represents the number of gallons of water (y) remaining in y −2.5x a 20-gallon tank being drained for number of minutes. The domain in this function would be x continuous. There would be an representing any point in time until the tank is drained so x-value connecting the points to form a straight line would be appropriate (Note: the context of the problem limits the values that can represent to positive values, since time cannot be negative.). x Functions can be represented as ordered pairs, tables, graphs, equations, physical models, or in words. Any given relationship can be represented using multiple representations. The equation = + defines a linear function whose graph (solution) is a straight line. The y mx b equation of a linear function can be determined given the slope, and the Verbal m, y-intercept, b. descriptions of practical situations that can be modeled by a linear function can also be represented using an equation. Example: Write the equation of a linear function whose slope is and is or y-intercept −4, located at the point (0, −4). The equation of this line can be found by substituting the values for the slope, = , and the m = into the general form of a linear function = + Thus, the equation y-intercept, b y mx b. −4, would be = 4. y x – Example: John charges a $30 flat fee to trouble shoot a personal watercraft that is not working properly and $50 per hour needed for any repairs. Write a linear function that represents the total cost, of a personal watercraft repair, based on the number of hours, y x, needed to repair it. Assume that there is no additional charge for parts. In this practical situation, the would be $30, to represent the initial flat fee to y-intercept, b, trouble shoot the watercraft. The slope, would be $50, since that would represent the rate m, per hour. The equation to represent this situation would be = 50x + 30. y
graph. Not all values for x could be represented and connecting the points would not be appropriate. Example: The function y = −2.5x + 20 represents the number of gallons of water (y) remaining in a 20-gallon tank being drained for x number of minutes. The domain in this function would be continuous. There would be an x-value representing any point in time until the tank is drained so connecting the points to form a straight line would be appropriate (Note: the context of the problem limits the values that x can represent to positive values, since time cannot be negative.). Functions can be represented as ordered pairs, tables, graphs, equations, physical models, or in words. Any given relationship can be represented using multiple representations. The equation y = mx + b defines a linear function whose graph (solution) is a straight line. The equation of a linear function can be determined given the slope, m, and the y-intercept, b. Verbal descriptions of practical situations that can be modeled by a linear function can also be represented using an equation. Example: Write the equation of a linear function whose slope is and y-intercept is −4, or located at the point (0, −4). The equation of this line can be found by substituting the values for the slope, m = , and the y-intercept, b = −4, into the general form of a linear function y = mx + b. Thus, the equation would be y = x – 4. Example: John charges a $30 flat fee to trouble shoot a personal watercraft that is not working properly and $50 per hour needed for any repairs. Write a linear function that represents the total cost, y of a personal watercraft repair, based on the number of hours, x, needed to repair it. Assume that there is no additional charge for parts. In this practical situation, the y-intercept, b, would be $30, to represent the initial flat fee to trouble shoot the watercraft. The slope, m, would be $50, since that would represent the rate per hour. The equation to represent this situation would be y = 50x + 30.
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