6 We interpret division by zero, in this case, to yield an infinite quotient with infinite meaning greater than any arbitrarily large value.
The relationship shown to the right is linear, but is perfectly vertical. Q is 14 regardless of the value of P. As we move from point C to point D, the value of P increases from 3 to 9, but Q remains at 14. In this case the rise is 6 but the run is zero. Using our formula for slope, rise ÷ run, we get 6 ÷ 0. Whatever points we use to compute the slope will lead to a run of zero or division by zero. In this case we say the slope is infinite.6
This is another case of a graph illustrating no relationship between P and Q; regardless of what value P takes on, Q remains fixed at 14.
6 We interpret division by zero, in this case, to yield an infinite quotient with infinite meaning greater than any arbitrarily large value.