Question

Your family is driving home from family vacation. After 3 hours, you have 23 gallons left in the tank and after 5 hours you have 19 gallons left. Write an equation to model the total gallons left, y, for driving x hours.

Answer 1

To model the total gallons left while driving x hours, use the equation y = -2x + 29, where y represents the total gallons left and x represents the hours driven.

Step-by-step explanation:

To write an equation to model the total gallons left while driving x hours, we can use a linear equation in the form y = mx + b, where y represents the total gallons left and x represents the hours driven.

Let's use the given information to find the slope and y-intercept.

From the first piece of information, after driving for 3 hours, there are 23 gallons left. This gives us the point (3, 23).

From the second piece of information, after driving for 5 hours, there are 19 gallons left. This gives us the point (5, 19).

We can now find the slope using the formula: slope (m) = (y2 - y1) / (x2 - x1).

The slope is: (19 - 23) / (5 - 3) = -2.

Next, we can substitute one of the given points and the slope into the equation y - y1 = m(x - x1) to find the y-intercept.

Using the point (3, 23) and the slope -2, we get: y - 23 = -2(x - 3).

Simplifying, we get y - 23 = -2x + 6.

Finally, rearranging the equation to the standard form, we have: y = -2x + 29.