Write the equation of the line that is perpendicular to the line x=3 and passes through the point (1,5)

Question

Write the equation of the line that is perpendicular to the line x=3 and passes through the point (1,5)

Answer 1

Hi Keith,

 

Here's a hint:

The line with the equation x=3 is a vertical line.

A line that is perpendicular to a vertical line is horizontal.

So what you need to find is the equation of a horizontal line (y=c) that passes through (1,5).

 

Hope this helps!

Answer 2

Keith,
Perpendicular lines are different in that their slopes are negative reciprocals of each other. In this case, the first line x = 3 has a vertical (undefined) slope... something like 1/0 which is impossible, but we can take the negative reciprocal of 1/0, which gives us -(0/1) or 0. So all that is left is determining where this horizontal line intersects the y-axis.

 

Because this line with slope, 0, passes through (1,5), it must also intersect the y-axis at 5, so the equation of our new line is:

 

y = 0x + 5, or

 

y = 5

 

Hope this helps!

Neal