slope intercept form from a table calculator

One example of function notation is an equation written in the slope-intercept form of a line, where x x is the input value, m m is the rate of change, and b b is the initial value of the dependent variable. Representing a Linear Function in Function NotationĪnother approach to representing linear functions is by using function notation. The train began moving at this constant speed at a distance of 250 meters from the station. As the time (input) increases by 1 second, the corresponding distance (output) increases by 83 meters. The rate of change for this example is constant, which means that it is the same for each input value. Recall that a rate of change is a measure of how quickly the dependent variable changes with respect to the independent variable. The train’s distance from the station is a function of the time during which the train moves at a constant speed plus its original distance from the station when it began moving at constant speed.For the train problem we just considered, the following word sentence may be used to describe the function relationship. Let’s begin by describing the linear function in words. Representing a Linear Function in Word Form We will describe the train’s motion as a function using each method. There are several ways to represent a linear function, including word form, function notation, tabular form, and graphical form. The function describing the train’s motion is a linear function, which is defined as a function with a constant rate of change. How can we analyze the train’s distance from the station as a function of time? In this section, we will investigate a kind of function that is useful for this purpose, and use it to investigate real-world situations such as the train’s distance from the station at a given point in time. Suppose a maglev train travels a long distance, and maintains a constant speed of 83 meters per second for a period of time once it is 250 meters from the station. It carries passengers comfortably for a 30-kilometer trip from the airport to the subway station in only eight minutes 2. Consider, for example, the first commercial maglev train in the world, the Shanghai MagLev Train ( Figure 1). Just as with the growth of a bamboo plant, there are many situations that involve constant change over time.

Figure 1 Shanghai MagLev Train (credit: 'kanegen'/Flickr)

Slope intercept form from a table calculator