Linear Equations Help



    Help on Linear Equations (slope, y-intercept, graphing)

     -   Since the presentation on linear equations ( f(x) or y = mx + b) is sometimes very time-limited at the end of the OCCC APPM 1313 Math for Health Careers course, here’s a link to an article on straight-line equations, including slope, y-intercept, and graphing from West Texas A&M University, Canyon, Texas.  This may help clarify the concepts.  (Don’t worry about the parallel and perpendicular lines part of the article.  That is “second semester stuff” for us.)

    Interpolation / Extrapolation Help

     -   On Worksheet 48, it's probably easier if you circle points A, B, and E to remind yourself that these are the actual data points.  The other points are not actual data points and probably shouldn't have the big heavy dots on them.

     -   To "interpolate" in question 2, go straight up from the x-axis at the 3 second mark until you reach the straight line.  Then go horizontally, left until you reach the y-axis.  The point on the y-axis, 300 meters, is the estimated distance the vehicle traveled at 3 seconds into the experiment (a race?).

     -   It's called "interpolation" because you're estimating the distance for 3 seconds based on actual data that's available both at less than 3 seconds (namely, 1 second) and at more than 3 seconds (namely, 4 seconds).  It's an estimate "between" ("inter" in Latin, like interstate:  between states) known data points.

     -   In question 3, the worksheet asks us to estimate the distance after 5 seconds.  We have data "below" 5 seconds, namely the 4 second value of 400 meters.  We don't have any data "above" 5 seconds, though.  Therefore, our estimate of 500 meters traveled in 5 seconds is "outside" ("extra" in Latin, like extramarital:  outside marriage) the existing data that we have.  Formally, the x value is outside the domain of known x-values.

     -   It's riskier to extrapolate from data than it is to interpolate.  For instance, we don't know for sure that the vehicle didn't hit a brick wall at 4.5 seconds.  If it did, 450 meters will be about as far as it ever goes from 4.5 seconds on, and our estimate for 5 seconds will be quite wrong.  Interpolation, on the other hand is less uncertain.  While the vehicle might have "spun out" between 2 and 3 seconds, it's highly unlikely that it would have attained 500 meters at the 5 second mark if it had spun out, so our interpolation of 300 meters as the distance corresponding to 3 seconds is much less risky than our extrapolation of 500 meters as the distance corresponding to 5 seconds.








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