Question

based on the data collected, which combination of gallons in the gas tank and maximum number of miles seems most likely to be possible?
0 gallons in the gas tank and 20 miles
9 gallons in the gas tank and 280 miles
11 gallons in the gas tank and 360 miles
19 gallons in the gas tank and 520 miles

Explanation:

Step1: Analyze the first option

If there are \(0\) gallons in the gas tank, the car can't run, so \(0\) gallons and \(20\) miles is impossible.

Step2: Analyze the second option

Looking at the graph, when \(x = 9\) (gallons), the value on the line is around \(240\) miles, not \(280\) miles.

Step3: Analyze the third option

When \(x = 11\) (gallons), if we assume the relationship is linear (since the graph looks linear - like a line of best - fit). If we take two points \((6,160)\) and \((12,320)\) from the line of best - fit. The slope \(m=\frac{320 - 160}{12 - 6}=\frac{160}{6}=\frac{80}{3}\approx26.67\). The equation of the line using the point - slope form \(y - y_1=m(x - x_1)\) with \((x_1,y_1)=(6,160)\) is \(y-160=\frac{80}{3}(x - 6)\), \(y=\frac{80}{3}x\). When \(x = 11\), \(y=\frac{80\times11}{3}=\frac{880}{3}\approx293.33\). Also, looking at the data points around \(x = 11\), \(360\) miles is in the range of the data spread.

Step4: Analyze the fourth option

The \(x\) - axis (gallons) only goes up to \(18\) (approximate maximum on the graph), so \(19\) gallons is beyond the scope of the data.

Answer:

11 gallons in the gas tank and 360 miles.