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What is the slope of the line perpendicular to this line: y=2x-3?

Answer 1

Any line with the slope of #-1/2# will be perpendicular to the given line.

#y = 2x -3# has a slope of #+ 2#, which means the line goes over #1# to the right and up #2# ( a positive slope). The inverse of 2 = 1/2 and the line must have a negative slope so the slope must be - 1/2. The y intercept of -3 does not matter. Any line with the slope of -1/2 will intercept the line at 90 degrees. y= - 1/2 + (x) is the answer.

Note that product of slopes of two perpendicular lines is always #-1#. An example is given below.

graph{(y-2x+3)(2y+x+3)=0 [-10, 10, -5, 5]}

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Answer 2

Jace Anderson

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. The original line has a slope of 2. So, the perpendicular line will have a slope of -1/2.

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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.