the graph shows the relationship between distance driven and gallons of gas used. use the graph to complete…

Explanation:

Step1: Find miles - per - gallon

The graph is a straight - line passing through the origin $(0,0)$. The slope of the line represents the miles per gallon. We can use two points on the line, say $(1,30)$ and $(0,0)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $y$ represents distance $d$ and $x$ represents gallons of gas $g$. So, $m=\frac{30 - 0}{1 - 0}=30$. The car gets 30 miles to the gallon.

Step2: Find distance for $2\frac{2}{3}$ gallons

We know the rate of miles per gallon is 30. To find the distance $d$ when the number of gallons $g = 2\frac{2}{3}=\frac{8}{3}$, we use the formula $d=mg$. Substitute $m = 30$ and $g=\frac{8}{3}$ into the formula: $d=30\times\frac{8}{3}=80$.

Answer:

The car gets 30 miles to the gallon. After the car has traveled 80 miles, $2\frac{2}{3}$ gallons of gas have been consumed.