Question

Write the equation of the line which passes through (2, 1) and is perpendicular to x = –2

Answer 1

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Answer 2

The line described by the equation x = -2 is a line completely vertical, straight up and down, at -2 on the x-axis. The points on this line go through every value of y, but only have x-values of -2. Lines perpendicular to this will be completely horizontal, and will be described by equations of the form y = k, where k is some constant value. The points on lines such as this will go through every value of x, but only have y-values of k. So we need to find the horizontal line which passes through your point (2, 1). This is the same as finding the value k for the equation y=k. You can see that the x-value, 2, does not matter, the line will pass through every x-value. However, all the points in the line have only a single y-value: k. So THIS point must have a y-value of k, and the y-value of this point is 1, so k must be equal to 1. So the line you're looking for is described by the equation:

y=1

It's good to realize, however, that you don't really need to go through this many logical steps to get the answer. If you can sort of "visualize" the situation described in your problem you can see that the answer to this question is basically found by just picking the y-value from the point they gave you: the question gives you a vertical line and a point, if you can visualize these two on a graph. Now visualize the perpendicular line (horizontal), and sort of 'slide it' up and down until it hits your point. That's the "common sense" way to think about this and makes the math much easier to understand.

Answer 3

Thank you!!!!!!!!!!(: