Question

The equation y = 450x represents the number of miles airplane Z traveled, y, for a flight of x hours. The graph below shows the number of miles airplane wtraveled for a 5-hour flight.

Answer 1

The plane Z distance travelled per hour can be modelled by the following equation:

`y_Z=450x`

This means that for every hour the plane travels 450 miles.

The plane W distance per hour is modelled by the linear graph showed in the picture. To determine it's equation we need to use two points, we will choose (1, 500) and (2, 1000). The equation is given by:

`\begin{gathered} y_W=(y_2-y_1)/(x_2-x_1)\cdot x \\ y_W=(1000-500)/(2-1)\cdot x \\ y_W=500\cdot x \end{gathered}`

This means that the plane W travels a distance of 500 miles per hour.

If the two planes travel for 2 hours, the plane W will be 100 miles farther than the plane Z, because:

`\begin{gathered} y_Z(2)=450\cdot2=900_{} \\ y_W(2)=500\cdot2=1000 \end{gathered}`