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How do you find the intercepts for # x=5#?

Answer 1

#x#-intercept: #(5,0)#
The line does not intersect the #y#-axis.

The graph of #x=5# is merely a straight vertical line, crossing the#x#-axis at #(5,0)# To think about this intuitively, #x=5# just means that #x# will always equal 5. There is no dependency on #y# whatsoever- so no matter what #y# is, #x# will always be 5.

In terms of intersection, this means that #x=5# will never even intersect the #y#-axis. #x=5# is a vertical line parallel to the vertical #y#-axis. In terms of #x#-intercepts, you can quite simply read it off the equation- When #x# equals 5, it intersects the #x#-axis ( at the point where #y#=0). You can also see on the graph that the point of intersection is #(5,0)#.

Note that #x=5# is not a function however. It does not pass the vertical line test- There are several #y#-values for a single #x#-value.

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Answer 2

Eva Adamson

To find the intercepts for the equation x = 5:

For the x-intercept, set y = 0 and solve for x. Since x is always 5, the x-intercept is (5, 0).
For the y-intercept, there is no y-variable involved, so it doesn't exist in this case.

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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.