What is the slope and y-intercept of the line #x=-6#?

Answer 1

The line is vertical.
It does not have a y-intercept at all.
The gradient is undefined (infinite).
This vertical line does not cross the #y-# axis anywhere.

#x = -6# is a vertical line crossing the x-axis at -6. It does not cross the y-axis at all, so there is no y-intercept.

Lines which are vertical are said to have an infinite or undefined gradient. The definition of gradient is #("change in y-values")/("change in x-values")#

As there is no change in the x-values the denominator would be 0. Vertical lines are only ones which cannot be written in the standard form of # y = mx + c# and are always given as #x = .....#

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Answer 2

Hazel Anglin

The line x = -6 is a vertical line parallel to the y-axis. Since it is parallel to the y-axis, it has no slope. The y-intercept does not exist for a vertical line.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.