Using Linear Models – Graphing a Linear Model Using the x- and y- Intercepts

This video is about using linear models. The exercise models how to write a linear model or linear equation for a given problem situation.

Suppose an airplane descends at a rate of 300 ft/min from an elevation of 8000 ft. Write and graph an equation to model the plane’s elevation as a function of the time it has been descending. Interpret the intercept at which the graph intersects the vertical axis.

To solve this problem, it is essential that one understands independent and dependent variables. Remember, when graphing on the coordinate plane, the independent variable is graphed along the x-axis and the dependent variable is graphed along the y-axis. As with most problems involving time, TIME is the independent variable and the countdown will start when the plane starts its decent. The plane’s elevation is the dependent variable. It has a distinct starting value of 8000 feet and it will be changing at a rate of -300 feet per minute. To find the plane’s elevation at any given time:

x = time elapsed measured in minutes

y = plane’s elevation measured in feet

The elevation equals the rate of descent times the time plus the starting elevation. The previous sentence translates into equation 1.

y = -300x + 8000                (1)

To graph this linear model, it would be best to use the x- and y-intercepts. The y-intercept will be          (0, 8000). This represents the beginning of the decent. The elapsed time is zero and the plane is at its starting elevation of 8000 feet. The x-intercept will is found by substituting 0 in for y in equation 1, giving equation 2.

0 = -300x + 8000                (2)

To find the x-intercept or the amount of time it will take the plane to land, add 300x to both sides of (2) to get:

300x = 8000         (3).

Divide both sides (3) by 3000:

x = 80/3 = 26.7 seconds            (4).

There are now two ordered pairs that can be graphed: (0, 8000) and (26.7, 0). See the video for the actual graphing.

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5 Responses

  1. […] To solve this problem, it is essential that one understands independent and dependent variables. Remember, when graphing on the coordinate plane, the independent variable is graphed along the x-axis and the dependent variable is graphed along the y-axis. For more on this problem using linear models. […]

  2. […] To solve this problem, it is essential that one understands independent and dependent variables. Remember, when graphing on the coordinate plane, the independent variable is graphed along the x-axis and the dependent variable is graphed along the y-axis. For more on this problem using linear models. […]

  3. […] To solve this problem, it is essential that one understands independent and dependent variables. Remember, when graphing on the coordinate plane, the independent variable is graphed along the x-axis and the dependent variable is graphed along the y-axis. For more on this problem using linear models. […]

  4. […] Using Linear Models – Graphing a Linear Model, Interpret the y-intercept Posted on October 30, 2009 by Site Admin This is the second post in the series on working with linear models. Here is the link to the first post: Using Linear Models – Graphing a Linear Model Using the x- and y-Intercepts […]

  5. […] Pilarski explains Graphing a Linear Model using x and y intercepts with video posted in his Algebra and Geometry […]

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