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Which equation represents the line that is perpendicular to y = 23 and passes through (-40,20)?

A. y = -15
B. y = 0
C. y = 5x + 52
D. y = -56

1 Answer

4 votes

Final answer:

The equation of a line perpendicular to y = 23 and passing through (-40,20) would be a vertical line x = -40. However, none of the provided answer choices represent a vertical line. Hence, there might be a mistake in the options provided, and none are correct answers.

Step-by-step explanation:

The problem is asking us to find the equation of a line that is perpendicular to y = 23 and passes through the point (-40,20). First, we note that y = 23 is a horizontal line because it has no x-dependence, so its slope is 0. A line that is perpendicular to a horizontal line is a vertical line, which can be represented by an equation of the form x = constant. Therefore, the equation of our line can only be x = -40 since x must be constant at the point (-40,20) for every value of y. From the given options, none of them exactly matches this form, suggesting a possible error in the options provided.

If we are constrained to choose from the provided options, we must look for the line that is vertical; unfortunately, none of the answer choices reflect a vertical line directly. However, options A (y = -15), B (y = 0), and D (y = -56) are all horizontal lines, so we can eliminate them. Option C (y = 5x + 52) has a non-zero slope and thus cannot be perpendicular to a horizontal line. By the process of elimination, none of the options given are correct, but if we had to choose the one that is closest to representing a vertical line, we unfortunately cannot as none match the requirement.

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