The relationship shown to the right is linear, but is perfectly vertical. We say that the slope of a vertical line is infinite.⁶ As shown to the right, 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. In other words, the slope is infinite.

    As before, this graph shows that there is no relationship between P and Q; regardless of what value P takes on, Q remains fixed at 14.


⁶ In mathematics infinite means existing beyond or being greater than any arbitrarily large value.

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