Ivanna starts her trip with 18 gallons of gas, and her car consumes 1 gallon for every 35 miles driven. We are asked to create an equation that relates $G$, the gallons of gas left, to $D$, the distance she has traveled.

Step-by-Step Solution:

1. Determine the initial amount of gas: Ivanna starts with 18 gallons, so when $D = 0$, $G = 18$.

2. Calculate the rate of gas consumption: The car uses 1 gallon every 35 miles, so the rate of gas consumption is $\frac{1}{35}$ gallons per mile.

3. Set up the linear equation:

   • For each mile driven, the gas in the tank decreases by $\frac{1}{35}$ gallon.
   • Therefore, the decrease in gas after traveling $D$ miles is $\frac{1}{35}D$.
   • The amount of gas left $G$ after driving $D$ miles is given by: $G = 18 - \frac{1}{35}D$

Final Equation:

The equation relating $G$ (gallons of gas left) to $D$ (distance traveled) is: $G = 18 - \frac{1}{35}D$

To graph this equation:

• Plot the starting point $(0, 18)$.
• Since the slope is $-\frac{1}{35}$, the line will slope downwards.
• The x-intercept, where $G = 0$, can be found by setting $G = 0$ in the equation and solving for $D$: $0 = 18 - \frac{1}{35}D$ Solving, we get $D = 18 \times 35 = 630$.

So, the line crosses the x-axis at $D = 630$, meaning Ivanna can travel 630 miles before running out of gas.

Would you like details on the graphing process or have any questions?

Further Questions

1. How can you determine the x-intercept for other similar equations?
2. How would the equation change if Ivanna’s car used gas more efficiently, say 1 gallon every 50 miles?
3. What would the graph look like if she started with only 10 gallons of gas?
4. How does a negative slope represent the gas consumption rate in this context?
5. Can this equation be used to calculate the gas left for any distance $D$?

Tip

When interpreting word problems, identify initial values and rates of change to help construct linear equations.