Question

The following graph represents the distance a commercial airplane travels over time, at cruising speed and an altitude of 35,000 feet. In fact, the distance the airplane travels at cruising speed is directly proportional to the time it travels. Using complete sentences, describe what the points (0, 0) and (4, 2268) represent.

Answer 1

If the quantities $x$ and $y$ are related by an equation $y=kx$ for some constant $k\not=0,$

we say that $y$ is directly proportional to $x.$ The constant $k$ is called the constant of proportionality.

Consider the point $(4, 2268)$

$$2268=k(4)$$

Solve for $k$

$$k=\dfrac{2268}{4}$$

$$k=567\ mi/hr$$

Point $(0,0)$

At time $t=0$ the airplane is at the start point.

We measure the distance travelled from the start point in miles. We measure the time in hours.

Point $(4,2268)$

The airplane is $2268$ miles from the start point after $4$ hours.