Let's examine the relationship between time [tex]\( t \)[/tex] and elevation [tex]\( e \)[/tex] using the given equation [tex]\( e = 300 - 10t \)[/tex].
1. For [tex]\( t = -2 \)[/tex]:
[tex]\[
e = 300 - 10(-2)
\][/tex]
Substituting [tex]\( t = -2 \)[/tex] into the equation:
[tex]\[
e = 300 + 20 = 320
\][/tex]
Therefore, [tex]\( a = 320 \)[/tex].
2. For [tex]\( t = 3.5 \)[/tex]:
[tex]\[
e = 300 - 10(3.5)
\][/tex]
Substituting [tex]\( t = 3.5 \)[/tex] into the equation:
[tex]\[
e = 300 - 35 = 265
\][/tex]
Thus, [tex]\( b = 265 \)[/tex] which is a viable value.
3. For [tex]\( t = 30 \)[/tex]:
[tex]\[
e = 300 - 10(30)
\][/tex]
Substituting [tex]\( t = 30 \)[/tex] into the equation:
[tex]\[
e = 300 - 300 = 0
\][/tex]
Therefore, [tex]\( c = 0 \)[/tex].
So, the values in the table of values for a linear equation are:
\begin{tabular}{|c|c|}
\hline
Time [tex]$(t)$[/tex] & Elevation [tex]$(e)$[/tex] \\
\hline
-2 & 320 \checkmark \\
\hline
3.5 & 265 \checkmark \\
\hline
30 & 0 \checkmark \\
\hline
\end{tabular}
Thus, the viable points and their values in the table are:
[tex]\[
\begin{array}{l}
a = 320 \checkmark \\
b = 265 \checkmark \\
c = 0 \quad \checkmark \\
\end{array}
\][/tex]
