Respuesta :
[tex]\bf \begin{array}{ccllll}
time(hours)&distance(miles)\\
-----&-------\\
0&2700\\
1&2160\\
2&1620\\
3&1080\\
4&540
\end{array}[/tex]
part A)
y-intercept is when the graph "intercepts" or touches the y-axis, and when that happens, x = 0, on that table, is the very first row, 0, 2700.
what does that mean? well, at 0 hours, the plane was 2700 miles away.
or another way to put it, the plane was still on the runway at the airport and hadn't taken off at 0 hours, and the airport where it was is 2700 miles away from its destination.
part B)
from the table, we can see the x = 1, y = 2160, and when x = 4, y = 540,
so our two points are (1, 2160) and (4, 540).
[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 1}}\quad ,&{{ 2160}})\quad % (c,d) &({{ 4}}\quad ,&{{ 540}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{540-2160}{4-1}\impliedby \begin{array}{llll} average\ rate\\ of\ change \end{array} \\\\\\ \cfrac{-1620}{3}\implies \boxed{-540}[/tex]
or -540/1, well the top is the rise(miles) and the bottom is the run(hours)... so it means -540 miles per each 1hour,
or
for every passing hour the plane is travelling, the distance from its origin and its destination is shrinking, namely, is getting closer to its destination.
part C)
well, we know for every hour is dropping by 540, so, 4hrs is 540, so 5hours it will drop another 540, or 540 - 540 = 0
so, the domain will be [0, 5], since after 5hours it'd be at its destination, because at 5hrs the miles away is 0, meaning it arrived at the destination.
part A)
y-intercept is when the graph "intercepts" or touches the y-axis, and when that happens, x = 0, on that table, is the very first row, 0, 2700.
what does that mean? well, at 0 hours, the plane was 2700 miles away.
or another way to put it, the plane was still on the runway at the airport and hadn't taken off at 0 hours, and the airport where it was is 2700 miles away from its destination.
part B)
from the table, we can see the x = 1, y = 2160, and when x = 4, y = 540,
so our two points are (1, 2160) and (4, 540).
[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 1}}\quad ,&{{ 2160}})\quad % (c,d) &({{ 4}}\quad ,&{{ 540}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{540-2160}{4-1}\impliedby \begin{array}{llll} average\ rate\\ of\ change \end{array} \\\\\\ \cfrac{-1620}{3}\implies \boxed{-540}[/tex]
or -540/1, well the top is the rise(miles) and the bottom is the run(hours)... so it means -540 miles per each 1hour,
or
for every passing hour the plane is travelling, the distance from its origin and its destination is shrinking, namely, is getting closer to its destination.
part C)
well, we know for every hour is dropping by 540, so, 4hrs is 540, so 5hours it will drop another 540, or 540 - 540 = 0
so, the domain will be [0, 5], since after 5hours it'd be at its destination, because at 5hrs the miles away is 0, meaning it arrived at the destination.
