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How do you write an equation in standard form for a line passing through (2, 1) and is perpendicular to x = –2?

Answer 1

#x=-2# represents a vertical line so that a perpendicular line to it will be a perfectly horizontal line passing through #(2,1)#.
A perfectly horizontal line has slope #m=0# (it is not increasing nor decreasing) so you can use your relationship:
#y-y_0=m(x-x_0)# with #m=0# giving:
#y-1=0(x-2)#
So your line has equation: #color(red)(y=1)#

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Answer 2

Jace Anderson

To write an equation in standard form for a line passing through the point (2, 1) and perpendicular to x = -2, first determine the slope of the perpendicular line. Since x = -2 is a vertical line, its slope is undefined. A line perpendicular to a vertical line is a horizontal line. The equation of a horizontal line passing through (2, 1) has the form y = constant. Therefore, the equation in standard form is y = 1.

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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.