Question

Use the information and graph for questions 6-9. The graph below shows the relationship between the number of gallons of ethanol-based gasoline and the number of gallons of regular gasoline sold at a gas station. Gasoline Sales (30, 3) Gallons of Ethanol (10, 1) X 30 20 10 Gallons of Gasoline 8 6 What is the unit rate for this proportional relationship? What does the point (30, 3) represent? A. The cost for 30 gallons of gasoline is $3. A. 0.1 gallon of gasoline per gallon of ethanol B. 0.1 gallon of ethanol per gallon of gasoline C. 10 gallons of gasoline per gallon of ethanol B. For every 30 gallons of gasoline sold 3 gallons of ethanol is sold. C. The cost for 3 gallons of gasoline is $30. D. For every 30 gallons of ethanol sold 3 gallons of gasoline is sold. D. 10 gallons of ethanol per gallon of gasoline 9 Which point is a point on the graph? 7 Which equation represents the proportional relationship? A. (2, 20) 307 A. y=3 B. y = 0 B. (20,20 C. (200,2) C. y= 10x D. (2,5) D. y= 30x

Answer 1

7.

Consider that the curve in the graph is a straight line.

The equation of a straight line passing through two points is given by,

`y-y_1=(y_2-y_1)/(x_2-x_1)*(x-x_1)`

From the graph, it is observed that the straight line passes through the points (10,1) and (30,3).

So the corresponding equation is given by,

`\begin{gathered} y-1=(3-1)/(30-10)*(x-10) \\ y-1=(2)/(20)*(x-10) \\ y-1=(1)/(10)*(x-10) \\ 10y-10=x-10 \\ 10y=x \\ y=(1)/(10)x \end{gathered}`

Thus, the equation governing the function is obtained.

Therefore, option B is the correct choice.