Question

phan fills the tank of her car with gasoline before starting her road trip. the table below shows the amount of gas left in her tank as she drives.

number of hours vs. amount left in tank
\

$$\begin{tabular}{|c|c|c|c|c|} \\hline \\begin{tabular}{c} number of hours spent \\\\ driving (h) \\end{tabular}$$

& 3 & 5 & 7 & 9 \\\\
\hline
\

$$\begin{tabular}{c} amount of gas left in \\\\ tank, in gallons (g) \\end{tabular}$$

& 12 & 8 & 4 & 0 \\\\
\hline
\end{tabular}

which equation models the amount of gas left in the car as phan drives, and how many gallons of gasoline does it take to fill her tank?

\\(g = 18 - 2h\\); 18 gallons
\\(g = 18 - 2h\\); 16 gallons
\\(g = 3h + 3\\); 30 gallons
\\(g = 3h + 3\\); 12 gallons

Explanation:

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<reasoning>

Calculate the rate of change (slope)

\[
m = \frac{g_2 - g_1}{h_2 - h_1} = \frac{8 - 12}{5 - 3} = \frac{-4}{2} = -2
\]

Determine the initial amount of gas (y-intercept)

\[

$$\begin{aligned} g &= mh + b \\ 12 &= -2(3) + b \\ 12 &= -6 + b \\ b &= 18 \end{aligned}$$

\]

Formulate the linear equation and identify the capacity

\[

$$\begin{aligned} g &= 18 - 2h \\ \text{At } h = 0, \quad g &= 18 \text{ gallons} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>g = 18 - 2h; 18 gallons</mcq-correct>
<mcq-option>g = 18 - 2h; 16 gallons</mcq-option>
<mcq-option>g = 3h + 3; 30 gallons</mcq-option>
<mcq-option>g = 3h + 3; 12 gallons</mcq-option>
</answer>

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Answer:

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<reasoning>

Calculate the rate of change (slope)

\[
m = \frac{g_2 - g_1}{h_2 - h_1} = \frac{8 - 12}{5 - 3} = \frac{-4}{2} = -2
\]

Determine the initial amount of gas (y-intercept)

\[

$$\begin{aligned} g &= mh + b \\ 12 &= -2(3) + b \\ 12 &= -6 + b \\ b &= 18 \end{aligned}$$

\]

Formulate the linear equation and identify the capacity

\[

$$\begin{aligned} g &= 18 - 2h \\ \text{At } h = 0, \quad g &= 18 \text{ gallons} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>g = 18 - 2h; 18 gallons</mcq-correct>
<mcq-option>g = 18 - 2h; 16 gallons</mcq-option>
<mcq-option>g = 3h + 3; 30 gallons</mcq-option>
<mcq-option>g = 3h + 3; 12 gallons</mcq-option>
</answer>

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