Question

lavaughn filled up his car with gas before embarking on a road trip across the country. let ( g ) represent the number of gallons of gas remaining in his gas tank after driving for ( t ) hours. the table below has select values showing the linear relationship between ( t ) and ( g ). determine the initial amount of gas in the tank.

( t )	( g )
3	7
6	4

answer attempt 1 out of 2
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Explanation:

Step 1: Find the slope (m)

The formula for slope between two points \((t_1, G_1)\) and \((t_2, G_2)\) is \(m=\frac{G_2 - G_1}{t_2 - t_1}\). Using the points \((1, 9)\) and \((3, 7)\):
\(m=\frac{7 - 9}{3 - 1}=\frac{-2}{2}=-1\)

Step 2: Use point - slope form to find the equation

The point - slope form is \(G - G_1=m(t - t_1)\). Using the point \((1, 9)\) and \(m=-1\):
\(G - 9=-1(t - 1)\)
Simplify the equation:
\(G - 9=-t + 1\)
\(G=-t + 10\)

Step 3: Find the initial amount (when \(t = 0\))

Substitute \(t = 0\) into the equation \(G=-t + 10\):
\(G=-0+10 = 10\)

Answer:

10