Question

airplane pilot: the graph below shows the rate at which fuel is burned when flying. use the amount of fuel used between hours 1.5 and 2.5 to make your slope calculation. the y - axis is the distance measured in nm, and the x - axis is the time measured in hours. write the equations for each line below. 1. high speed cruise: y = x 2. long range cruise: y = x time and fuel vs. distance conditions: 800 lb. payload, isa, zero wind, nbaa ifr reserves

Explanation:

Step1: Recall slope - formula for line equation

The equation of a line is $y = mx + b$. For lines passing through the origin (which we assume here as at $t = 0$, $d=0$), the equation simplifies to $y=mx$, where $m$ is the slope. The slope $m=\frac{\Delta y}{\Delta x}$, with $\Delta y$ being the change in distance and $\Delta x$ being the change in time.

Step2: Calculate slope for high - speed cruise

For high - speed cruise, at $x_1 = 1.5$ hours, $y_1=578$ nm and at $x_2 = 2.5$ hours, $y_2 = 980$ nm.
$\Delta y=y_2 - y_1=980 - 578 = 402$ nm, $\Delta x=x_2 - x_1=2.5 - 1.5 = 1$ hour.
The slope $m_1=\frac{\Delta y}{\Delta x}=\frac{402}{1}=402$. So the equation is $y = 402x$.

Step3: Calculate slope for long - range cruise

For long - range cruise, at $x_1 = 1.5$ hours, $y_1 = 527$ nm and at $x_2 = 2.5$ hours, $y_2=887$ nm.
$\Delta y=y_2 - y_1=887 - 527 = 360$ nm, $\Delta x=x_2 - x_1=2.5 - 1.5 = 1$ hour.
The slope $m_2=\frac{\Delta y}{\Delta x}=\frac{360}{1}=360$. So the equation is $y = 360x$.

Answer:

1. High speed cruise: $y = 402x$
2. Long range cruise: $y = 360x$