Two airplanes, flying at the same altitude, are tracked using the same coordinate system on a radar screen. One plane is following a path described by the equation $y = \frac { 2 } { 3 } x - 4$ , and the other is following a path described by the equation $2 x = 3 y + 9$ . Is there a possibility of a collision?
A) yes
B) no

Question

Quizplus · Accepted Answer

To determine if there is a possibility of collision, we need to find if the two planes will ever intersect. We can set the two equations equal to each other and solve for x:
\begin{align*}
\frac{2}{3}x-4 &= \frac{3}{2}y+9 \
\frac{2}{3}x &= \frac{3}{2}y+13 \
x &= \frac{9}{4}y+19.5
\end{align*}
Now we see that the x-coordinate of the intersection point is solely dependent on the y-coordinate. Therefore, the two planes will never intersect at a single point, and there is no possibility of a collision. Thus, the answer is B.

Two Airplanes, Flying at the Same Altitude, Are Tracked Using y=23x−4y = \frac { 2 } { 3 } x - 4y=32​x−4

Two Airplanes, Flying at the Same Altitude, Are Tracked Using $y = \frac { 2 } { 3 } x - 4$