Question

Scientists are preparing two satellites to be launched. The equation y = 4600x represents the number of miles, y, that the satellite, Space Explorer A, flies in x. The Table below represents the number of miles, y, that the satellite, Space Explorer B, flies in x hours.Hours (x) Miles (y)5 1500020 6000022 6600024 72000How many fewer miles does Space Explorer B travel in one hour than Space Explorer A?

Answer 1

Answer: We have a linear equation that represents the number of miles that satellite A flies in one hour, which is:

(A)

$y(x)=4600x$

So, In one hour this satellite flies:

$y(1)=4600(1)=4600\text{ miles}$

(B)

The linear equation for satellite B can be extracted from the given table as follows:

Slope:

$\begin{gathered} y_B(x)=mx+b \\ \rightarrow\therefore\rightarrow \\ m=\frac{\Delta y}{\Delta x}=\frac{60,000-15,000}{20-5}=\frac{45,000}{15}=3000 \\ \end{gathered}$

Y-Intercept:

$\begin{gathered} y_B(x)=mx+b \\ \rightarrow\therefore\rightarrow \\ y_B(5)=3000(5)+b=15,000 \\ \rightarrow\therefore\rightarrow b=15,000-36,000=-21,000 \\ \\ \therefore\rightarrow \\ y_B(x)=3000x-21,000 \end{gathered}$

Miles, that the Satellite (B) travels in one hour are:

$y_B(1)=3000(1)-21,000=3000-21,000=-18,000$

The difference in the miles traveled by these two space explorers are:

$y_B(1)-y_A(1)=-18,000mi-3000mi=-15,000$

Therefore this is the answer

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