**Linear
Equations Help**

**ChuckOates.com**

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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