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.)
/ 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.
"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
- 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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