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Question

Consider the line y=6x-1. Find the equation of the line that is parallel to this line and passes through the point 2, 6.

 

Find the equation of the line that is perpendicular to this line and passes through the point 2, 6
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Answer 1

Any parallel line has an equation that differs from the given one only by it constant term, i.e., it is y = 6x + c for some constant c which you need to find. Finding c is easy - it must be such that the line equation is satisfied by the point (2,6). That is

 

6 = 6*2 + c

 

Hence, c = -6 and the equation is y = 6x - 6.

 

The slope of any perpendicular line equals the negative reciprocal of the given line's slope. Since the given line has slope of 6, the perpendicular lines have slope of -1/6 and hence equations of the form

 

y = (-1/6)*x  + d,

 

where d is constant that you need to find. Just as above you can plug in the point (2,6) and solve for d:

 

6 = (-1/6)*2 + d

 

Hence, d = 6 + 1/3 = 19/3 and the equation is y = (-1/6)*x + 19/3.

 

 

 

 

Answer 2

For a line parallel to y=6x-1, it must have a general form of

y = 6x+z, where z is a real number.

If this line passes (2,6), we simply plug 2 into x and 6 into y into the general form to find the corresponding z:

6 = 6 * 2 + z,    z=-6

so the line is: y=6x-6