Question

phan fills the tank of her car with gasoline before starting her road trip. the table below shows the amount of gas left in her tank as she drives. number of hours vs. amount left in tank number of hours spent driving (h) 3 5 7 9 amount of gas left in tank, in gallons (g) 12 8 4 0 which equation models the amount of gas left in the car as phan drives, and how many gallons of gasoline does it take to fill her tank? g = 18 – 2h; 18 g = 18 – 2h; 16 g = 3h 3; 30 g = 3h 3; 12

Answer 1

G(h)    h
12      3
8        5
4        7
0        9

Equation of the line:

slope = [12-0]/[3-9] = 12 / -6 = -2

g / [h - 9] = -2

g = -2(h-9)

g = -2h + 18

g = 18 -2h

Filling the tank ==> h = 0

g = 18 - 2(0) = 18

Answer: first option g = 18 -2 h; 18

Answer 2

Answer:

Option B) 18, $g = 18 - 2h$

Step-by-step explanation:

We are given the following:

Number of hours spent driving (h):     3       5        7        9

      Amount of gas left in tank (g):      12     8        4        0  

We have to find the equation that models the amount of gas left in the car as Phan drives.

We can find the equation with the help of two-point form of equation of straight line.

The equation of line is given by:

$(y-y_1) = \displaystyle\frac{y_2-y_2}{x_2-x_1}(x-x_1)$

where, $(x_1,y_1), (x_2.y_2)$ is the point through which the line passes.

(9,0), (7,4)

The equation of line is:

$(g-0) = \displaystyle\frac{4 - 0}{7-9}(h-9)\\\\-2g = 4h - 36\\\Rightarrow g = 18 - 2h$

Gallons of gasoline required to fill the tank =

we put h = 0 in the equation.

$g = 18 - 2h\\g = 18-2(0)\\g = 18$

Thus, 18 gallons of gasoline is required to fill up the tank.

Option B) 18, $g = 18 - 2h$