find the equation of a line prependicular to x=-2, passing through the point (1, -3)

2 Answers

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The line x = -2 is a line that has a value of x equal to -2 for all values of y. This is a vertical line. The line perpendicular to x = -2, would have to be a horizontal line. We also know that the line we need passes through the point (1, -3). Therefore we need a horizontal line that has the value of y equal to -3 for all values of x. This line is y = -3.

Therefore the required equation of a line perpendicular to x=-2 and passing through the point (1, -3) is y = -3.

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neela | High School Teacher | (Level 3) Valedictorian

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Any line perpendicular to x= -2 is of the form y = k, as x = -2 is perpendicular to x-axis. So a line y = k is || to x-axis.

Since the point (1,-3) is on this line y = k, the coordinates of this point (1,-3) should satisfy the equation of the line y = k:

=> -3 = k.

=> k = -3.

Therefore y = -3 is the line which is perpendicular to x= -2 and passes through the point (1,-3).