Question

1. karl filled up the tank of his truck with 400l of fuel and set it up to deliver a shipment of bananas to alaska. the track consumed 0.8l of fuel for each kilometer driven. write the equation of a linear function. graph the amount of fuel remaining in the trucks tank (in liters) as the function of distance (in kilometers)

a) how much fuel does he have left after 100km?
b) how many kilometers could he drive on 100l?

Explanation:

Step1: Define linear function

Let $x$ = distance (km), $y$ = fuel left (L). Initial fuel: 400L, fuel consumption: 0.8L/km.
Function: $y = 400 - 0.8x$

Step2: Calculate fuel after 100km

Substitute $x=100$ into the function.
$y = 400 - 0.8(100) = 400 - 80$

Step3: Calculate km for 100L fuel left

Set $y=100$, solve for $x$.
$100 = 400 - 0.8x \implies 0.8x = 400 - 100 \implies x = \frac{300}{0.8}$

Answer:

a) 320 liters
b) 375 kilometers

Graph Instructions (for the linear function):

• Plot the y-intercept at $(0, 400)$ (starting fuel, 0 km driven).
• Plot the x-intercept: set $y=0$, $0=400-0.8x \implies x=500$, so point $(500, 0)$.
• Draw a straight line connecting these two points to represent the function $y=400-0.8x$.