Exercise 2 Page 195

We want to graph the following equation. In this equation, $y$ is the distance traveled in miles on $x$ gallons of gas by the car that the Thompson family is buying. We know that the distance traveled varies directly with the number of gallons of gas used. Recall that a relationship is a direct variation when the ratio of $y$ to $x$ is constant. Direct variation equations follow a specific format. Note that the given equation follows this format. Therefore, this is a direct variation equation and it is represented by a straight line on a coordinate plane. To graph the line, we need to find two points that lie on the line. Since $(0,0)$ is one solution of $y=mx,$ the graph of a direct variation always passes through the origin. In addition, we know that the car can travel $70$ $\text{miles}$ on $2$ $\text{gallons}$ of gas. Therefore, the line passes through the points $(0,0)$ and $(2,70).$ Let's draw this line!

Now we will find how many miles per gallon the car gets. Since this situation is represented by the direct variation equation, the value of the slope tells us how many miles per gallon of gas the car can drive. In this case, the value of the slope is $35.$ Therefore, the car can get $35$ miles per gallon of gas.