A positive, nonlinear realtionship

   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.

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